Speed of Travelling Wave NEET Questions

Physics - Oscillations and Waves

Speed of Travelling Wave MCQ Questions


1.
The speed of a travelling wave is determined by tracking a point of constant phase. For the wave y = a sin(kx − ωt), the condition 'constant phase' means:
A.
kx − ωt = constant, so that differentiating with respect to time gives k(dx/dt) = ω, hence wave speed v = dx/dt = ω/k
B.
y = constant, so the particle velocity equals wave speed
C.
a = constant, meaning amplitude never changes
D.
t = constant, meaning the wave is frozen in time
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ANSWER :
A. kx − ωt = constant, so that differentiating with respect to time gives k(dx/dt) = ω, hence wave speed v = dx/dt = ω/k
2.
For a progressive wave y = a sin(kx − ωt), the wave speed v expressed in terms of wavelength λ and time period T is:
A.
v = λ × T
B.
v = T/λ
C.
v = λ/T = λν
D.
v = 1/(λT)
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ANSWER :
C. v = λ/T = λν
3.
All three expressions — v = ω/k, v = λ/T, and v = λν — represent the wave speed. Which correctly identifies the physical meaning of v = λ/T?
A.
v = λ/T only applies to transverse waves, not longitudinal waves
B.
The ratio of wavelength to period gives the particle velocity
C.
In one time period T (one complete oscillation of a particle), the wave pattern advances by exactly one wavelength λ
D.
In one wavelength of distance, one complete oscillation occurs in time T
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ANSWER :
C. In one time period T (one complete oscillation of a particle), the wave pattern advances by exactly one wavelength λ
4.
The relationship v = λν shows that for a given wave speed v in a medium, if the frequency ν is doubled, the wavelength λ:
A.
Halves (λ = v/ν → if ν doubles, λ = v/(2ν) = λ_original/2)
B.
Remains the same
C.
Doubles
D.
Quadruples
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ANSWER :
A. Halves (λ = v/ν → if ν doubles, λ = v/(2ν) = λ_original/2)
5.
The speed of a mechanical wave is determined by:
A.
The frequency of the source generating the wave
B.
The wavelength of the wave
C.
The elastic and inertial properties of the medium (e.g., tension and linear mass density for a string), NOT by the wave's amplitude, frequency or wavelength
D.
The amplitude of the wave — larger amplitudes travel faster
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ANSWER :
C. The elastic and inertial properties of the medium (e.g., tension and linear mass density for a string), NOT by the wave's amplitude, frequency or wavelength
6.
The formula for the speed of transverse waves on a stretched string with tension T and linear mass density μ is derived using dimensional analysis. The dimensions of T/μ are:
A.
[T/μ] = [MLT⁻²]/[ML⁻¹] = [L²T⁻²], so √(T/μ) has dimensions [LT⁻¹] = m/s ✓
B.
[T/μ] = [M²L⁻¹T⁻²], so √(T/μ) has dimensions [MLT⁻¹]
C.
[T/μ] = [L²T⁻¹], so √(T/μ) has dimensions [LT⁻¹/²]
D.
[T/μ] = [MLT⁻²], same dimensions as force
😑 View Answer Rough Work Error
ANSWER :
A. [T/μ] = [MLT⁻²]/[ML⁻¹] = [L²T⁻²], so √(T/μ) has dimensions [LT⁻¹] = m/s ✓