Beats
Beats are loud-soft variations caused by superposition of two nearby frequencies. Beat frequency is |f1 - f2|.
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Beats and Doppler Effect
Class 11 Physics notes covering beats, beat frequency, Doppler effect, moving source, moving observer, applications, numericals and PYQs.
CBSEJEE MainJEE AdvancedIBICSEIGCSEA-LevelOlympiad
Important Exam Note
NEET 2026 Syllabus Status
Important Note: Doppler Effect is not part of the NEET 2026 syllabus. The status of NEET 2027 and future syllabi may change depending on NMC updates. However, Doppler Effect remains important for JEE Main, JEE Advanced, Olympiads, IB, IGCSE and A-Level Physics.
Doppler Effect
Apparent frequency changes because source and observer motion changes wavefront spacing or receiving rate.
Sign Discipline
Draw source and observer arrows first. Approach increases frequency; separation decreases frequency.
Concept
Introduction
Beats and Doppler Effect are two beautiful applications of superposition and relative motion in sound. Beats explain waxing and waning loudness when two nearby frequencies combine. Doppler Effect explains why apparent frequency changes when source, observer or both move.
Important Note: Doppler Effect is not part of the NEET 2026 syllabus. The status of NEET 2027 and future syllabi may change depending on NMC updates. However, Doppler Effect remains important for JEE Main, JEE Advanced, Olympiads, IB, IGCSE and A-Level Physics.
Real-life examples include tuning a guitar using beats, ambulance siren pitch changing as it passes, train horn pitch shift, police radar, aircraft motion and astronomical red shift.
Exam perspective: beats questions are usually short and formula-based, while Doppler questions test sign convention, relative approach, source motion versus observer motion and apparent frequency.
Exam FocusMemory trick: beats need nearby frequencies; Doppler needs relative motion.
Exam FocusDoppler for NEET 2026: note syllabus exclusion, but study for JEE/IB/A-Level/Olympiad.
Concept
Beats
Beats are periodic variations in loudness heard when two sound waves of nearly equal frequencies and comparable amplitudes superpose. The sound alternately becomes loud and soft.
Suppose two waves are y1 = A sin(2πf1t) and y2 = A sin(2πf2t). On adding them, the resultant can be written as a fast oscillation multiplied by a slowly varying amplitude factor.
Using sin C + sin D = 2 sin((C+D)/2) cos((C-D)/2), resultant displacement becomes y = 2A cos[π(f1-f2)t] sin[2π((f1+f2)/2)t].
The amplitude factor changes slowly, so intensity and loudness rise and fall. Maximum loudness occurs when waves are in phase; minimum loudness occurs when they are nearly opposite in phase.
Beat frequency is fb = |f1 - f2|. It tells the number of loud beats heard per second.
Real-life example: when a tuning fork of 256 Hz and another of 258 Hz are sounded together, 2 beats per second are heard.
Exam FocusBeat frequency is frequency difference.
Exam FocusBeats are heard clearly only when frequency difference is small.
Exam FocusAdd displacements, not loudness.
Concept
Applications of Beats
Beats are used to tune musical instruments. A musician compares an instrument note with a standard tuning fork. If beats are heard, frequencies are not equal. As tuning improves, beat frequency decreases to zero.
In laboratories, beats help detect small frequency differences that are difficult to measure directly. Counting beats per second gives the difference between two frequencies.
Sound engineering uses beating to identify unwanted frequency mismatch, phase issues and modulation-like effects in audio systems.
Real-life example: two guitar strings meant to produce the same note create a wavering sound if one is slightly out of tune. Tightening or loosening one string reduces the beat frequency.
Common mistake: if beat frequency is 4 Hz and one source is 256 Hz, the other source may be 252 Hz or 260 Hz unless extra information is given.
Exam FocusZero beats means equal frequencies.
Exam FocusBeat frequency alone gives two possible unknown frequencies.
Exam FocusTuning means reducing beats.
Concept
Doppler Effect
Doppler Effect is the apparent change in frequency heard by an observer due to relative motion between source and observer along the line joining them.
The actual frequency emitted by the source does not change. What changes is the rate at which wavefronts reach the observer.
When source and observer move towards each other, wavefronts are received more frequently and apparent frequency increases. When they move away from each other, apparent frequency decreases.
The compact formula is f' = f[(v ± v0)/(v ∓ vs)], but signs must be selected from physical approach or separation, not blindly.
Real-life example: an ambulance siren sounds higher pitched when approaching and lower pitched after passing.
Exam FocusApproach increases apparent frequency.
Exam FocusSeparation decreases apparent frequency.
Exam FocusSource motion changes wavelength; observer motion changes receiving rate.
Concept
Moving Source
When the source moves, it changes spacing of wavefronts in front and behind. In front of an approaching source, wavefronts are compressed and wavelength decreases. Behind a receding source, wavefronts are stretched.
Source moving towards stationary observer: f' = fv/(v - vs). Source moving away: f' = fv/(v + vs).
Physical meaning: the source emits each next crest from a new position. If it moves toward the observer, crests are closer together; if it moves away, crests are farther apart.
Common trap: source velocity appears in denominator because source motion changes effective wavelength.
Example: a train horn moving toward a platform observer is heard at higher pitch.
Exam FocusSource toward observer: denominator decreases.
Exam FocusSource away: denominator increases.
Exam FocusSource motion changes wavelength.
Concept
Moving Observer
When the observer moves, the emitted wavelength in the medium is unchanged if source is stationary, but the observer cuts wavefronts at a different rate.
Observer moving towards stationary source: f' = f(v + v0)/v. Observer moving away: f' = f(v - v0)/v.
Physical meaning: moving towards wavefronts increases the number of crests received per second. Moving with the wavefronts decreases the receiving rate.
Common trap: observer velocity appears in numerator because observer motion changes the rate of receiving waves.
Example: a cyclist moving towards a stationary siren hears a higher pitch.
Exam FocusObserver toward source: numerator increases.
Exam FocusObserver away: numerator decreases.
Exam FocusObserver motion changes encounter rate.
Concept
Combined Cases
General one-dimensional Doppler formula can be remembered as f' = f(v ± v0)/(v ∓ vs). Choose signs so approach increases f' and separation decreases f'.
Source and observer moving towards each other: use larger numerator and smaller denominator, so apparent frequency increases strongly.
Source and observer moving away from each other: use smaller numerator and larger denominator, so apparent frequency decreases strongly.
Source chasing observer: if source is behind and faster than observer, separation decreases, apparent frequency increases; if observer is faster, separation increases, apparent frequency decreases.
Observer chasing source: if observer gains on source, separation decreases; if not, separation increases. Always draw arrows before formula.
Exam FocusDraw line diagram first.
Exam FocusApproach means frequency up.
Exam FocusSeparation means frequency down.
Concept
Applications of Doppler Effect
Ambulance and police sirens show Doppler pitch shift as they approach and recede. The sudden change after passing is a classic real-life observation.
Radar speed guns use Doppler shift in reflected electromagnetic waves to measure vehicle speed. Similar ideas are used in aircraft tracking and weather radar.
Astronomy uses Doppler shift of light to detect motion of stars and galaxies. Red shift indicates recession; blue shift indicates approach.
Medical Doppler ultrasound measures blood flow by detecting frequency shift of reflected ultrasound from moving blood cells.
In aircraft and train motion, Doppler shift helps estimate relative speeds and explain observed changes in pitch.
Exam FocusRadar uses reflected Doppler shift.
Exam FocusMedical ultrasound uses Doppler flow measurement.
Exam FocusSiren pitch shift is sound Doppler.
Signs
Doppler Sign Convention Table
| Situation | Use | Reason | Common Mistake |
|---|---|---|---|
| Observer moving towards source | +v0 in numerator | Observer meets more wavefronts per second. | Putting observer speed in denominator. |
| Observer moving away from source | -v0 in numerator | Observer meets fewer wavefronts per second. | Using plus just because observer is moving. |
| Source moving towards observer | -vs in denominator | Wavelength ahead decreases. | Adding vs for approach. |
| Source moving away from observer | +vs in denominator | Wavelength reaching observer increases. | Confusing source and observer formulas. |
Formula
Premium Formula Cards
fb = |f1 - f2|Number of loud beats heard per second.
f' = f[(v ± v0)/(v ∓ vs)]Choose signs from approach or separation.
f' = f(v + v0)/vStationary source, moving observer.
f' = f(v - v0)/vReceiving rate decreases.
f' = fv/(v - vs)Wavelength in front becomes smaller.
f' = fv/(v + vs)Wavelength reaching observer becomes larger.
NCERT/JEE Style
Beats and Doppler Diagrams
Diagrams use black wavefronts and red arrows/labels for clear sign-convention reading.
Beat Formation
Beat Amplitude Graph
Moving Source Wavefronts
Case 1: Observer Moving Towards Stationary Source
Case 2: Observer Moving Away From Stationary Source
Case 3: Source Moving Towards Stationary Observer
Case 4: Source Moving Away From Stationary Observer
Case 5: Source and Observer Moving Towards Each Other
Case 6: Source and Observer Moving Away From Each Other
Case 7: Source Chasing Observer
Case 8: Observer Chasing Source
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Solved
40 High-Quality Solved Numericals
Each numerical tests a different idea: beats, ambiguity, tuning, moving source, moving observer, combined motion, chasing cases, reflected Doppler, radar and graph-based beat reading.
Numerical 1JEE Main Easy
Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. Find beat frequency.
Show Solution
Given: f1=256 Hz, f2=260 Hz
Formula: fb=|f1-f2|
Solution: fb=|256-260|=4 Hz
Final Answer: 4 Hz
Numerical 2JEE Main Easy
A tuning fork of 512 Hz produces 3 beats per second with another fork. Find possible frequencies of the other fork.
Show Solution
Given: f=512 Hz, fb=3 Hz
Formula: unknown = f ± fb
Solution: possible frequencies = 512±3 = 509 Hz or 515 Hz
Final Answer: 509 Hz or 515 Hz
Numerical 3JEE Main Easy
A fork produces 5 beats/s with 300 Hz fork. On filing it, beat frequency decreases. Find original frequency if filing increases frequency.
Show Solution
Given: standard=300 Hz, beats=5, filing increases f and beats decrease
Formula: original was below standard
Solution: f = 300 - 5 = 295 Hz
Final Answer: 295 Hz
Numerical 4JEE Main Medium
Two waves y1=A sin(2π250t) and y2=A sin(2π254t) superpose. Find beat frequency.
Show Solution
Given: f1=250 Hz, f2=254 Hz
Formula: fb=|f1-f2|
Solution: fb=4 Hz
Final Answer: 4 Hz
Numerical 5JEE Main Medium
A listener hears 6 beats/s when two sources are used. One source is 440 Hz. If the other is known to be lower, find it.
Show Solution
Given: f=440 Hz, beat=6 Hz, other lower
Formula: unknown=440-6
Solution: unknown=434 Hz
Final Answer: 434 Hz
Numerical 6JEE Main Medium
Two nearby frequencies have average frequency 500 Hz and beat frequency 8 Hz. Find the frequencies.
Show Solution
Given: (f1+f2)/2=500, |f1-f2|=8
Formula: frequencies = average ± beat/2
Solution: f = 500 ± 4 = 496 Hz, 504 Hz
Final Answer: 496 Hz and 504 Hz
Numerical 7JEE Main Medium
A stationary observer hears a source of 500 Hz moving towards him at 34 m/s. Speed of sound is 340 m/s. Find apparent frequency.
Show Solution
Given: f=500, v=340, vs=34
Formula: f'=fv/(v-vs)
Solution: f'=500×340/(340-34)=555.6 Hz
Final Answer: 555.6 Hz
Numerical 8JEE Main Medium
A 500 Hz source moves away from stationary observer at 34 m/s. v=340 m/s. Find apparent frequency.
Show Solution
Given: f=500, v=340, vs=34
Formula: f'=fv/(v+vs)
Solution: f'=500×340/374=454.5 Hz
Final Answer: 454.5 Hz
Numerical 9JEE Main Medium
Observer moves towards stationary 600 Hz source at 20 m/s. Speed of sound is 340 m/s. Find apparent frequency.
Show Solution
Given: f=600, v=340, v0=20
Formula: f'=f(v+v0)/v
Solution: f'=600×360/340=635.3 Hz
Final Answer: 635.3 Hz
Numerical 10JEE Main Medium
Observer moves away from stationary 600 Hz source at 20 m/s. Speed of sound is 340 m/s. Find apparent frequency.
Show Solution
Given: f=600, v=340, v0=20
Formula: f'=f(v-v0)/v
Solution: f'=600×320/340=564.7 Hz
Final Answer: 564.7 Hz
Numerical 11JEE Main Difficult
Source and observer move towards each other. f=800 Hz, v=340 m/s, vs=30 m/s, v0=20 m/s. Find f'.
Show Solution
Given: f=800, v=340, vs=30, v0=20
Formula: f'=f(v+v0)/(v-vs)
Solution: f'=800×360/310=929.0 Hz
Final Answer: 929 Hz
Numerical 12JEE Main Difficult
Source and observer move away from each other. f=800 Hz, v=340 m/s, vs=30 m/s, v0=20 m/s. Find f'.
Show Solution
Given: f=800, v=340, vs=30, v0=20
Formula: f'=f(v-v0)/(v+vs)
Solution: f'=800×320/370=691.9 Hz
Final Answer: 691.9 Hz
Numerical 13JEE Advanced
A source behind observer chases him. Source speed 40 m/s, observer speed 20 m/s, f=700 Hz, v=340 m/s. Find f'.
Show Solution
Given: source behind, both same direction, source faster; source approaches observer
Formula: f'=f(v-v0)/(v-vs)
Solution: f'=700×(340-20)/(340-40)=746.7 Hz
Final Answer: 746.7 Hz
Numerical 14JEE Advanced
Observer behind source chases it. Observer speed 40 m/s, source speed 20 m/s, f=700 Hz, v=340 m/s. Find f'.
Show Solution
Given: observer behind, observer faster; separation decreases
Formula: f'=f(v+v0)/(v+vs)
Solution: f'=700×(340+40)/(340+20)=738.9 Hz
Final Answer: 738.9 Hz
Numerical 15JEE Advanced
Observer behind source but slower. Observer speed 10 m/s, source speed 30 m/s, f=700 Hz, v=340 m/s. Find f'.
Show Solution
Given: separation increases
Formula: f'=f(v+v0)/(v+vs)
Solution: f'=700×350/370=662.2 Hz
Final Answer: 662.2 Hz
Numerical 16JEE Advanced
A source moving at 20 m/s towards a wall emits 500 Hz. Find beat frequency between direct and reflected sound heard by source. v=340 m/s.
Show Solution
Given: moving source receives echo from stationary wall; apparent reflected frequency has double Doppler
Formula: fecho=f(v+vs)/(v-vs)
Solution: fecho=500×360/320=562.5 Hz; beats=62.5 Hz
Final Answer: 62.5 Hz
Numerical 17JEE Advanced
A police radar receives reflected frequency shift approximately 2vf/c. If f=10 GHz, car speed=30 m/s, c=3×108 m/s, find shift.
Show Solution
Given: f=1010 Hz, u=30, c=3×108
Formula: Δf=2uf/c
Solution: Δf=2×30×1010/(3×108)=2000 Hz
Final Answer: 2000 Hz
Numerical 18JEE Advanced
An approaching train horn appears 550 Hz and receding appears 450 Hz to stationary observer. Find train speed if v=340 m/s.
Show Solution
Given: fa=fv/(v-u), fr=fv/(v+u)
Formula: ratio=550/450=(v+u)/(v-u)
Solution: 11/9=(340+u)/(340-u); u=34 m/s
Final Answer: 34 m/s
Numerical 19JEE Advanced
A source frequency is unknown. When approaching stationary observer at 34 m/s apparent frequency is 550 Hz. v=340. Find source frequency.
Show Solution
Given: f'=fv/(v-vs)
Formula: f=f'(v-vs)/v
Solution: f=550×306/340=495 Hz
Final Answer: 495 Hz
Numerical 20JEE Advanced
A moving observer hears 408 Hz from stationary 400 Hz source. v=340. Find observer speed and direction.
Show Solution
Given: f'=f(v±v0)/v, f'>f so towards
Formula: v0=v(f'/f-1)
Solution: v0=340(408/400-1)=6.8 m/s
Final Answer: 6.8 m/s towards source
Numerical 21IB
Two notes of 440 Hz and 442 Hz are played. How many loud sounds per second?
Show Solution
Given: f1=440, f2=442
Formula: beat frequency=|f1-f2|
Solution: 2 beats/s
Final Answer: 2
Numerical 22IB
A siren frequency 1000 Hz approaches observer at 25 m/s. v=350 m/s. Find apparent frequency.
Show Solution
Given: f=1000, v=350, vs=25
Formula: f'=fv/(v-vs)
Solution: f'=1000×350/325=1076.9 Hz
Final Answer: 1076.9 Hz
Numerical 23IGCSE
A car horn recedes from a stationary listener. Does pitch increase or decrease?
Show Solution
Given: source receding
Formula: separation increases, frequency decreases
Solution: pitch decreases
Final Answer: decreases
Numerical 24IGCSE
Two tuning forks produce 3 beats/s. One is 256 Hz. Give possible second frequencies.
Show Solution
Given: f=256, beat=3
Formula: unknown=f±beat
Solution: 253 Hz or 259 Hz
Final Answer: 253 Hz or 259 Hz
Numerical 25A-Level
A source approaches at Mach 0.1. If f=1000 Hz and observer stationary, find f' using vs=0.1v.
Show Solution
Given: vs=0.1v
Formula: f'=fv/(v-vs)=f/(0.9)
Solution: f'=1111.1 Hz
Final Answer: 1111.1 Hz
Numerical 26A-Level
An observer moves towards a stationary source at 0.05v. If source frequency is 800 Hz, find observed frequency.
Show Solution
Given: v0=0.05v
Formula: f'=f(1+0.05)
Solution: f'=840 Hz
Final Answer: 840 Hz
Numerical 27Olympiad
A source and observer move perpendicular to line joining them at that instant. What is first-order Doppler shift?
Show Solution
Given: radial relative velocity zero
Formula: Doppler depends on radial component
Solution: First-order shift is zero
Final Answer: zero
Numerical 28Olympiad
A source emits pulses every 0.01 s and moves towards observer at 10% of wave speed. Find received period for stationary observer.
Show Solution
Given: T=0.01 s, vs=0.1v
Formula: f'=f/(1-0.1), so T'=T(1-0.1)
Solution: T'=0.009 s
Final Answer: 0.009 s
Numerical 29Conceptual Numerical
Two forks initially produce 8 beats/s. Wax is attached to one fork and beats become 5/s. If wax lowers frequency and standard is 300 Hz, find original fork frequency assuming waxed fork was above standard.
Show Solution
Given: standard=300, original beat=8, wax lowers and beat decreases
Formula: original above standard
Solution: f=308 Hz
Final Answer: 308 Hz
Numerical 30Conceptual Numerical
A 500 Hz siren passes a stationary observer. Just before passing apparent frequency is 550 Hz. Just after passing is approximately what if source speed same and v=340? First find speed.
Show Solution
Given: 550=500×340/(340-u)
Formula: 340-u=309.09, u=30.91
Solution: receding f'=500×340/(340+30.91)=458.3 Hz
Final Answer: 458.3 Hz
Numerical 31Conceptual Numerical
Observer moving with same speed and direction as source, separation constant. What is observed frequency in still air if both move at 20 m/s and observer is in front? f=600, v=340.
Show Solution
Given: source behind, observer in front, same speed
Formula: f'=f(v-v0)/(v-vs)
Solution: v0=vs, so ratio=1
Final Answer: 600 Hz
Numerical 32Conceptual Numerical
Source and observer move together towards left with same speed, observer behind source. Find apparent frequency relative to f.
Show Solution
Given: same velocity, separation constant
Formula: Doppler ratio becomes 1 for same line velocity
Solution: f'=f
Final Answer: same as source frequency
Numerical 33Graph Numerical
A beat amplitude graph shows 10 maxima in 5 s. Find beat frequency and frequency difference.
Show Solution
Given: 10 beats in 5 s
Formula: fb=N/t
Solution: fb=2 Hz; difference=2 Hz
Final Answer: 2 Hz
Numerical 34Graph Numerical
Beat maxima are separated by 0.25 s. Find beat frequency.
Show Solution
Given: Tbeat=0.25 s
Formula: fb=1/Tbeat
Solution: fb=4 Hz
Final Answer: 4 Hz
Numerical 35Mixed
An observer hears 4 beats/s between a 500 Hz fork and a Doppler-shifted 480 Hz siren. Find apparent siren frequency possibilities.
Show Solution
Given: beat=4 with 500 Hz
Formula: f'=500±4
Solution: 496 or 504 Hz; but siren source actual 480 context may need motion details
Final Answer: 496 Hz or 504 Hz
Numerical 36Mixed
A source recedes so apparent frequency is 90% of original for stationary observer. Find source speed as fraction of v.
Show Solution
Given: f'/f=v/(v+vs)=0.9
Formula: v+vs=v/0.9
Solution: vs=(1/0.9-1)v=v/9
Final Answer: v/9
Numerical 37Mixed
Observer recedes so apparent frequency is 90% of original. Find observer speed as fraction of v.
Show Solution
Given: f'/f=(v-v0)/v=0.9
Formula: v0=0.1v
Solution: 0.1v
Final Answer: undefined
Numerical 38Mixed
A source approaches so apparent frequency is 125% of original. Find source speed fraction of v.
Show Solution
Given: f'/f=v/(v-vs)=1.25
Formula: v-vs=0.8v
Solution: vs=0.2v
Final Answer: 0.2v
Numerical 39Mixed
Observer approaches so apparent frequency is 125% of original. Find observer speed fraction of v.
Show Solution
Given: f'/f=(v+v0)/v=1.25
Formula: v0=0.25v
Solution: 0.25v
Final Answer: 0.25v
Numerical 40Reasoning Numerical
If beat frequency is zero between two tuning forks, what is their frequency relation?
Show Solution
Given: fb=0
Formula: fb=|f1-f2|
Solution: |f1-f2|=0, so f1=f2
Final Answer: equal frequencies
Numerical 41Reasoning Numerical
A listener moving away at speed of sound from a stationary source hears what frequency classically?
Show Solution
Given: v0=v away
Formula: f'=f(v-v0)/v
Solution: f'=0
Final Answer: zero
Numerical 42Reasoning Numerical
A source moves toward stationary observer at speed approaching v. What happens to classical f'?
Show Solution
Given: vs approaches v
Formula: f'=fv/(v-vs)
Solution: denominator approaches zero, f' becomes very large
Final Answer: tends to infinity classically
Numerical 43Reasoning Numerical
Two forks have frequencies 301 Hz and 299 Hz. Average pitch heard is approximately what and beat frequency?
Show Solution
Given: f1=301, f2=299
Formula: average=(f1+f2)/2, beat=|f1-f2|
Solution: average=300 Hz, beat=2 Hz
Final Answer: 300 Hz, 2 Hz
Question Bank
64 PYQs and Exam Questions
Question 1JEE Main
Define beats.
Show Answer
Periodic waxing and waning of sound intensity due to superposition of two nearly equal frequencies.
Question 2JEE Main
Write beat frequency formula.
Show Answer
fb = |f1 - f2|.
Question 3JEE Main
Why should frequencies be close for beats to be heard distinctly?
Show Answer
If difference is large, loudness variations are too rapid to perceive as beats.
Question 4JEE Main
A 256 Hz fork gives 4 beats/s with another fork. Possible frequencies?
Show Answer
252 Hz or 260 Hz.
Question 5JEE Main
What happens to beat frequency as tuning becomes perfect?
Show Answer
It becomes zero.
Question 6JEE Main
Define Doppler Effect.
Show Answer
Apparent change in observed frequency due to relative motion of source and observer.
Question 7JEE Main
When source approaches observer, apparent frequency?
Show Answer
Increases.
Question 8JEE Main
When source recedes, apparent frequency?
Show Answer
Decreases.
Question 9JEE Main
Observer moving towards source formula?
Show Answer
f' = f(v+v0)/v.
Question 10JEE Main
Source moving towards observer formula?
Show Answer
f' = fv/(v-vs).
Question 11JEE Advanced
Why does source velocity appear in denominator?
Show Answer
Moving source changes wavelength in the medium.
Question 12JEE Advanced
Why does observer velocity appear in numerator?
Show Answer
Moving observer changes rate of encountering wavefronts.
Question 13JEE Advanced
What component of velocity matters in Doppler Effect?
Show Answer
Component along line joining source and observer.
Question 14JEE Advanced
What is first-order Doppler shift for transverse motion?
Show Answer
Zero in classical sound Doppler if radial component is zero.
Question 15JEE Advanced
Can actual source frequency change in Doppler Effect?
Show Answer
No, apparent frequency changes for observer.
Question 16IB
Give an everyday Doppler example.
Show Answer
Ambulance siren pitch changes as it passes.
Question 17IB
What causes higher pitch for approaching source?
Show Answer
Wavefronts reach observer more frequently.
Question 18IB
What are beats used for in music?
Show Answer
Tuning instruments.
Question 19IB
What does zero beat indicate?
Show Answer
Equal frequencies.
Question 20IB
What is apparent frequency?
Show Answer
Frequency received or measured by observer.
Question 21ICSE
If two forks differ by 2 Hz, beats per second?
Show Answer
2.
Question 22ICSE
Pitch of receding siren is higher or lower?
Show Answer
Lower.
Question 23ICSE
Pitch of approaching siren is higher or lower?
Show Answer
Higher.
Question 24ICSE
What is the condition for beats?
Show Answer
Two sound waves of nearly equal frequencies.
Question 25ICSE
What is beat period?
Show Answer
Time interval between successive loud sounds; Tb=1/fb.
Question 26IGCSE
A car horn approaches a listener. What happens to wavelength in front?
Show Answer
It decreases.
Question 27IGCSE
Does Doppler shift occur without relative motion along line of sight?
Show Answer
No first-order shift for sound if radial relative velocity is zero.
Question 28IGCSE
What is used to detect speed in police radar?
Show Answer
Doppler shift.
Question 29IGCSE
What is used in medical blood flow measurement?
Show Answer
Doppler ultrasound.
Question 30IGCSE
If observer moves with wave speed away from source, what is heard?
Show Answer
Classically zero frequency.
Question 31A-Level
State general Doppler formula for sound.
Show Answer
f' = f(v ± v0)/(v ∓ vs) with signs chosen by approach/separation.
Question 32A-Level
How is beat frequency obtained from superposition identity?
Show Answer
The slowly varying amplitude envelope has frequency equal to difference of component frequencies.
Question 33A-Level
What is phase relation at beat maximum?
Show Answer
Waves are in phase.
Question 34A-Level
What is phase relation at beat minimum?
Show Answer
Waves are out of phase.
Question 35A-Level
Can Doppler Effect occur for light?
Show Answer
Yes, but relativistic treatment is needed for high speeds.
Question 36Olympiad
What happens when source speed exceeds sound speed?
Show Answer
Shock waves and Mach cone form; simple subsonic formula fails.
Question 37Olympiad
What is sonic boom related to?
Show Answer
Supersonic motion and overlapping wavefronts.
Question 38Olympiad
Why is radar Doppler shift doubled in reflection?
Show Answer
Wave is shifted during incidence and again during reflection from moving target.
Question 39Olympiad
For astronomy, recession causes what shift?
Show Answer
Red shift.
Question 40Olympiad
Approach causes what shift in light?
Show Answer
Blue shift.
Question 41Assertion-Reason
Assertion: Beats are used for tuning instruments. Reason: Beat frequency becomes zero when frequencies become equal.
Show Answer
Both true and reason explains assertion.
Question 42Assertion-Reason
Assertion: Approaching source is heard at higher frequency. Reason: Wavefronts in front are closer together.
Show Answer
Both true and reason explains assertion.
Question 43Assertion-Reason
Assertion: Observer velocity appears in denominator. Reason: Observer motion changes wavelength.
Show Answer
Both false as stated; observer velocity appears in numerator and changes encounter rate.
Question 44Assertion-Reason
Assertion: Doppler Effect changes actual source frequency. Reason: Source emits different frequency when moving.
Show Answer
Assertion false; apparent frequency changes.
Question 45True/False
Beat frequency is sum of two frequencies.
Show Answer
False.
Question 46True/False
Beat frequency is absolute difference of frequencies.
Show Answer
True.
Question 47True/False
Doppler Effect depends on relative motion along line of sight.
Show Answer
True.
Question 48True/False
Receding source gives higher apparent frequency.
Show Answer
False.
Question 49True/False
Approaching observer hears higher frequency from stationary source.
Show Answer
True.
Question 50Case Study
An ambulance approaches, passes, and recedes. Describe pitch change.
Show Answer
High pitch while approaching, sudden change near passing, lower pitch while receding.
Question 51Case Study
Two guitar strings produce slow beats. What should a musician do?
Show Answer
Adjust tension until beats disappear.
Question 52Case Study
Police radar detects reflected frequency shift. What is measured?
Show Answer
Vehicle speed.
Question 53Case Study
Aircraft approaches a listener at high speed. What happens to apparent frequency?
Show Answer
It increases while approaching.
Question 54Case Study
A star shows red shift. What does it suggest?
Show Answer
It is receding from observer.
Question 55Conceptual
Why are two possible frequencies possible in beat problems?
Show Answer
Because |f1-f2| gives a difference, not whether unknown is above or below.
Question 56Conceptual
Why draw arrows before Doppler formula?
Show Answer
To decide approach/separation and signs correctly.
Question 57Conceptual
What is the biggest Doppler sign mistake?
Show Answer
Putting source and observer velocities in wrong numerator/denominator or wrong sign.
Question 58Conceptual
How are beats related to superposition?
Show Answer
They arise from superposition of nearby frequency waves.
Question 59Conceptual
Difference between pitch change by Doppler and actual source frequency change?
Show Answer
Doppler changes received frequency; source frequency remains same.
Question 60Reasoning
Why does apparent frequency increase when observer moves towards source?
Show Answer
Observer meets more wavefronts per second.
Question 61Reasoning
Why does apparent frequency decrease when source moves away?
Show Answer
Wavefront spacing reaching observer is larger.
Question 62Reasoning
Why is beat loudness periodic?
Show Answer
Relative phase between two nearby frequencies changes periodically.
Question 63Reasoning
Why are beats not clear if frequencies differ by hundreds of hertz?
Show Answer
Amplitude changes too rapidly for ear to perceive separate beats.
Case Study
Case Study Practice
Case Study 1: Ambulance Siren
An ambulance siren approaches and then moves away from a stationary observer.
Question 1: Which effect explains pitch change?
Doppler Effect.
Question 2: When is pitch higher?
During approach.
Question 3: When is pitch lower?
During recession.
Case Study 2: Train Horn
A train horn of fixed frequency moves towards a platform.
Question 1: Does actual horn frequency change?
No.
Question 2: What changes for observer?
Apparent frequency.
Question 3: Which formula if observer stationary?
f'=fv/(v-vs).
Case Study 3: Musical Tuning
Two strings of nearly equal frequencies produce 3 beats/s.
Question 1: What is frequency difference?
3 Hz.
Question 2: What happens at perfect tuning?
Beat frequency becomes zero.
Question 3: Why are beats useful?
Small frequency differences become audible.
Case Study 4: Police Radar
Radar wave reflects from a moving vehicle.
Question 1: Which principle is used?
Doppler shift.
Question 2: Why is reflected shift larger?
Shift occurs in going and returning wave.
Question 3: What quantity is measured?
Vehicle speed.
Case Study 5: Aircraft Motion
An aircraft approaches a listener and then passes overhead.
Question 1: Before passing, apparent frequency?
Higher than emitted.
Question 2: After passing, apparent frequency?
Lower than emitted.
Question 3: What matters most?
Radial component of relative velocity.
Mistakes
Common Mistakes
- Wrong sign convention: decide approach or separation before formula.
- Confusing source and observer motion: source velocity changes wavelength; observer velocity changes receiving rate.
- Wrong Doppler formula usage: source speed belongs in denominator, observer speed in numerator.
- Beat frequency mistakes: beat frequency is absolute difference, not sum or average.
- Frequency vs wavelength confusion: approaching source compresses wavelength and increases apparent frequency.
Revision
Quick Revision Notes
- Beats occur for nearly equal frequencies.
- Beat frequency = |f1 - f2|.
- Beat maxima occur when waves are in phase.
- Doppler Effect is apparent frequency change due to relative motion.
- Approach increases apparent frequency.
- Separation decreases apparent frequency.
- Observer velocity appears in numerator.
- Source velocity appears in denominator.
- Source towards: v - vs.
- Source away: v + vs.
- Observer towards: v + v0.
- Observer away: v - v0.
- Draw arrows before applying signs.
- Radar and medical ultrasound use Doppler shift.
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