Standing Waves in Strings and Organ Pipes, Fundamental Mode and Harmonics, Beats NEET Questions

Physics - Oscillations and Waves

Standing Waves in Strings and Organ Pipes, Fundamental Mode and Harmonics, Beats MCQ Questions


1.
Standing waves are formed by the superposition of:
A.
Two waves of same frequency travelling in the same direction with a phase difference
B.
Two waves of different frequencies travelling in the same direction
C.
A single wave reflecting between two boundaries without superposition
D.
Two identical sinusoidal waves of the same frequency and amplitude travelling in opposite directions in the same medium
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ANSWER :
D. Two identical sinusoidal waves of the same frequency and amplitude travelling in opposite directions in the same medium
2.
The equation of a standing wave formed by superposition of y₁ = a sin(kx − ωt) and y₂ = a sin(kx + ωt) is:
A.
y = a² sin(kx) cos(ωt)
B.
y = 2a cos(kx) sin(ωt)
C.
y = 2a sin(kx) cos(ωt)
D.
y = 2a sin(kx − ωt)
😑 View Answer Rough Work Error
ANSWER :
C. y = 2a sin(kx) cos(ωt)
3.
The key distinguishing feature of a standing wave y = 2a sin(kx) cos(ωt) compared to a progressive wave y = a sin(kx − ωt) is:
A.
A standing wave can only exist in solids, not in gases
B.
A standing wave has larger amplitude than a progressive wave
C.
A standing wave has double the frequency of the constituent progressive waves
D.
In a standing wave, kx and ωt appear separately (not combined as kx±ωt), so the pattern does not travel; amplitude varies with position
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ANSWER :
D. In a standing wave, kx and ωt appear separately (not combined as kx±ωt), so the pattern does not travel; amplitude varies with position
4.
NODES in a standing wave y = 2a sin(kx) cos(ωt) are positions where:
A.
cos(ωt) = 0 at certain times, making displacement zero momentarily
B.
The amplitude is maximum: sin(kx) = 1 → x = (2n+1)λ/4
C.
The amplitude is permanently zero: sin(kx) = 0 → x = nλ/2 for n = 0,1,2,…
D.
The particle velocity is maximum at all times
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ANSWER :
C. The amplitude is permanently zero: sin(kx) = 0 → x = nλ/2 for n = 0,1,2,…
5.
ANTINODES in a standing wave are positions where the amplitude is maximum (= 2a). They are located at:
A.
x = (2n−1)λ/2 for n = 1, 2, 3,…
B.
x = (2n+1)λ/4 for n = 0, 1, 2, 3,… — midway between consecutive nodes
C.
x = nλ for n = 0, 1, 2, 3,…
D.
x = nλ/2 for n = 0, 1, 2, 3,…
😑 View Answer Rough Work Error
ANSWER :
B. x = (2n+1)λ/4 for n = 0, 1, 2, 3,… — midway between consecutive nodes
6.
In a standing wave, all particles between two consecutive nodes oscillate:
A.
With different phases and different amplitudes
B.
With the SAME phase (they all reach maximum simultaneously) but with DIFFERENT amplitudes depending on their position
C.
Randomly with no fixed phase or amplitude relationship
D.
With the same phase and the same amplitude 2a
😑 View Answer Rough Work Error
ANSWER :
B. With the SAME phase (they all reach maximum simultaneously) but with DIFFERENT amplitudes depending on their position