Correct Answer: Option (1)
Waves NEET MCQs
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Waves Formula Sheet
Important formulas from transverse wave equation, string tension, sound waves, standing waves, organ pipes, beats and Doppler effect.
1. Basic Wave Terms
- v = fλ = λ/T = ω/k
- f = 1/T, ω = 2πf = 2π/T
- k = 2π/λ is propagation constant or wave number.
- Angular phase: φ = kx ± ωt + φ0
- Path difference and phase difference: Δφ = 2πΔx/λ
- Time difference and phase difference: Δφ = 2πΔt/T = ωΔt
2. Progressive Wave Equation
- Wave in +x direction: y = A sin(ωt - kx + φ)
- Wave in -x direction: y = A sin(ωt + kx + φ)
- General travelling wave: y = F(x - vt) or F(x + vt)
- Wave equation: ∂2y/∂x2 = (1/v2)∂2y/∂t2
- At fixed x, particle executes SHM: a = -ω2y
3. Particle Motion in a Wave
- Particle velocity: u = ∂y/∂t
- Maximum particle velocity: umax = Aω
- Particle acceleration: a = ∂2y/∂t2
- Maximum particle acceleration: amax = Aω2
- Slope of waveform: dy/dx, maximum slope: Ak
- Relation for transverse wave: u = -v(dy/dx) for +x wave.
4. Wave Speed in Medium
- General mechanical wave speed: v = sqrt(elastic property / inertial property)
- Transverse wave on string: v = sqrt(T/μ)
- Longitudinal wave in solid rod: v = sqrt(Y/ρ)
- Sound in liquid: v = sqrt(B/ρ)
- Newton formula for gas: v = sqrt(P/ρ)
- Laplace correction: v = sqrt(γP/ρ) = sqrt(γRT/M)
5. String, Tension and Linear Density
- Linear mass density: μ = m/L = ρA
- For circular wire: μ = ρπr2
- String wave speed: v = sqrt(T/μ)
- If tension is due to load: T = Mg
- Frequency of stretched string: f = (1/2L)sqrt(T/μ)
- Proportionality: f ∝ (1/L)sqrt(T/μ)
6. Hanging String or Rope
- Tension at a point with length x below it: T = μxg
- Wave speed at that point: v = sqrt(gx)
- Speed at middle of rope of length L: v = sqrt(gL/2)
- Time from bottom to top of hanging rope: t = 2sqrt(L/g)
- Time from bottom to height x: t = 2sqrt(x/g)
7. Waves on Stretched String
- Both ends fixed: L = nλ/2
- Allowed wavelength: λn = 2L/n
- Harmonic frequency: fn = nv/2L
- Fundamental frequency: f1 = v/2L
- All harmonics are present: fn = nf1
- Number of loops in nth harmonic = n
8. Standing Waves
- Standing wave form: y = 2A sin kx cos ωt
- Node condition: sin kx = 0
- Antinode condition: |sin kx| = 1
- Distance between adjacent nodes: λ/2
- Distance between adjacent antinodes: λ/2
- Distance between nearest node and antinode: λ/4
- No net energy transfer in an ideal standing wave.
9. Open Organ Pipe
- Both ends are antinodes.
- Length condition: L = nλ/2
- Frequency: fn = nv/2L, n = 1, 2, 3...
- Fundamental: f1 = v/2L
- pth overtone: f = (p + 1)v/2L
- All harmonics are present.
10. Closed Organ Pipe
- Closed end is node and open end is antinode.
- Length condition: L = (2n - 1)λ/4
- Frequency: fn = (2n - 1)v/4L, n = 1, 2, 3...
- Fundamental: f1 = v/4L
- pth overtone: f = (2p + 1)v/4L
- Only odd harmonics are present.
11. End Correction and Resonance Tube
- End correction: e ≈ 0.6r
- Open pipe effective length: Leff = L + 2e
- Closed pipe effective length: Leff = L + e
- First resonance: l1 + e = λ/4
- Second resonance: l2 + e = 3λ/4
- l2 - l1 = λ/2, so v = 2f(l2 - l1)
12. Sound Speed and Temperature
- In gas: v = sqrt(γRT/M)
- At temperature t degree C: vt = v0sqrt((273 + t)/273)
- Approximation in air: v ≈ 331 + 0.61t m/s
- Sound speed is independent of pressure for ideal gas at fixed temperature.
- Speed increases with temperature.
- Speed in moist air is greater than speed in dry air.
13. Sound Pressure Wave
- Displacement wave: s = s0 sin(ωt - kx)
- Pressure wave: ΔP = ΔP0 cos(ωt - kx)
- Pressure and displacement differ by phase π/2.
- Pressure amplitude: ΔP0 = Bks0
- Bulk modulus relation: B = -V(dP/dV)
14. Intensity and Loudness
- Intensity: I = Power/Area
- Point source: I = P/4πr2
- Inverse square law: I ∝ 1/r2
- Sound level: β = 10 log10(I/I0) dB
- Reference intensity: I0 = 10-12 W m-2
- Difference: β2 - β1 = 10 log10(I2/I1)
15. Superposition and Interference
- Resultant amplitude: R = sqrt(A12 + A22 + 2A1A2cosφ)
- Phase of resultant: tanθ = A2sinφ/(A1 + A2cosφ)
- Constructive interference: Δx = nλ, Δφ = 2nπ
- Destructive interference: Δx = (2n + 1)λ/2, Δφ = (2n + 1)π
- Coherent sources: same frequency and constant phase difference.
16. Beats
- Beat frequency: fb = |f1 - f2|
- Beat period: Tb = 1/fb
- For amplitudes A1 and A2: Amax = A1 + A2
- Amin = |A1 - A2|
- Intensity ratio: Imax/Imin = (A1 + A2)2/(A1 - A2)2
17. Doppler Effect in Sound
- General formula: f' = f (v ± vo)/(v ∓ vs)
- Observer moving towards source: f' = f(v + vo)/v
- Observer moving away from source: f' = f(v - vo)/v
- Source moving towards observer: f' = fv/(v - vs)
- Source moving away from observer: f' = fv/(v + vs)
- Source and observer approaching: f' = f(v + vo)/(v - vs)
- Source and observer receding: f' = f(v - vo)/(v + vs)
18. Doppler Special Cases
- With wind along sound direction, use effective speed v ± w.
- Echo from a stationary wall for moving source towards wall: fecho = f(v + vs)/(v - vs)
- Beat heard due to direct and reflected sound: fb = |fecho - f|
- Doppler effect in light, low speed: Δf/f ≈ v/c
- Relativistic light Doppler approach: f' = f sqrt((c + v)/(c - v))
19. Reflection and Refraction of Waves
- Frequency remains unchanged during reflection and refraction.
- At fixed end or denser medium reflection: phase change π.
- At free end or rarer medium reflection: no phase reversal.
- Refraction relation: sin i/sin r = v1/v2 = λ1/λ2
- When medium changes: v and λ change, f remains same.
20. Useful Ratios and Shortcuts
- For same string material and tension: v ∝ 1/r
- For same material and radius: v ∝ sqrt(T)
- For same tension and length: f ∝ 1/sqrt(μ)
- For sonometer: n = (1/2L)sqrt(T/μ)
- If length is divided into parts: 1/f = 1/f1 + 1/f2 + 1/f3 for string segments in series by lengths.
- Octave means frequency ratio 2:1; three octaves means 8:1.
Section A - Easy Questions
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (4)
Section B - Moderate Questions
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (1)
Section C - Previous Years NEET Questions
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (4)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (3)
Correct Answer: Option (3)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (1)
Section D - Assertion - Reason Type Questions
Correct Answer: Option (2)
Correct Answer: Option (4)
Correct Answer: Option (3)
Correct Answer: Option (4)
Correct Answer: Option (2)
Correct Answer: Option (3)
Correct Answer: Option (2)
Correct Answer: Option (1)
Correct Answer: Option (1)
Correct Answer: Option (2)
Correct Answer: Option (2)
Correct Answer: Option (2)
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