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1. Two waves travelling in a medium in the *x*-direction are represented by
*y*_{1} = Asin(α*t* - β*x*) and y_{2} = Acos(β*x* + α*t* - π/4), where *y*_{1} and *y*_{2} are the displacements of the particles of the medium, *t* is time, and α and β are constants. The two waves have different

Correct Answers :

[B]

Explanation :

2. A sine wave has an amplitude *A* and a wavelength *λ*. Let *V* be
the wave velocity, and *ν* be maximum velocity of a particle in the medium.

Correct Answers :

[B]

Explanation :

3. The equation y = acos^{2}(2*πnt* - 2*πx*/λ) represents a wave with

Correct Answers :

[D]

Explanation :

4. The displacement due to a wave moving in the positive
x-direction is given by at time

*t* = 0 and by at *t*=2 seconds, where *x* and *y* are in meters. The velocity of the wave in m/s is

Correct Answers :

[A]

Explanation :

5. A wave represented by the equation y = *a*cos (*kx* - ω*t*) is
superposed with another wave to form a stationary wave such that the point *x* = 0 is a node. The equation for the other wave is

Correct Answers :

[C]

Explanation :

6. A wave travelling in a material medium is described by the
equation *y* = *A*sin(*kx* - ωt). The maximum particle velocity is

Correct Answers :

[A]

Explanation :

7. A metal string is fixed between rigid supports. It is initially at
negligible tension. Its Young modulus is γ, density is ρ and coefficient of thermal expansion is α . If it is now cooled through
a temperature = *t*, transverse waves will move along it with
speed

Correct Answers :

[C]

Explanation :

8. Two identical strings are stretched at tensions T_{A} and T_{B}. A
tuning fork is used to set them in vibration. A vibrates in its fundamental mode and B in its second harmonic mode.

Correct Answers :

[B]

Explanation :

9. The tension of a string is increased by 44%. If its frequency of
vibration is to remain unchanged, its length must be increased by

Correct Answers :

[D]

Explanation :

10. In a sonometer wire, the tension is maintained by suspending a
50.7-kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m^{3}. The fundamental frequency of the
wire is 260 Hz. If the suspended mass is completely submerged in water, the fundamental frequency will become

Correct Answers :

[D]

Explanation :

11. A string of length 0.4 m and mass 10^{-2} kg is clamped at its ends.
The tension in the string is 1.6 N. When a pulse travels along the string, the shape of the string is found to be the same at times t
and *t* + Δ*t*. The value of Δ*t* is

Correct Answers :

[B]

Explanation :

12. A string A has double the length, double the tension, double the
diameter and double the density as another string B. Their fundamental frequencies of vibration are n_{A} and n_{B} respectively. The ratio n_{A}/n_{B} is equal to

Correct Answers :

[A]

Explanation :

13. The extension in a string obeying Hooke’s law is *x*. The speed of
transverse waves in the stretched string is *ν*. If the extension in the string is increased to 1.5x, the speed of transverse waves in it will be

Correct Answers :

[A]

Explanation :

14. A cylindrical resonance tube, open at both ends, has a fundamental frequency *F* in air. Half of the length of the tube is dipped vertically in water. The fundamental frequency of the air column now is

Correct Answers :

[C]

Explanation :

15. An open pipe is suddenly closed at one end, as a result of which
the frequency of the third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open
pipe. The fundamental frequency of the open pipe is

Correct Answers :

[A]

Explanation :

16. The third overtone of an open organ pipe of length l_{o} has the
same frequency as the third overtone of a closed pipe of length l_{c}. The ratio l_{o} / l_{c} is equal to

Correct Answers :

[D]

Explanation :

17. A pipe of length 1 m is closed at one end. The velocity of sound
in air is 300 m/s. The air column in the pipe will not resonate for sound of frequency

Correct Answers :

[C]

Explanation :

18. Two closed organ pipes, A and B, have the same length. A is
wider than B. They resonate in the fundamental mode at frequencies n_{A} and n_{B} respectively.

Correct Answers :

[C]

Explanation :

19. An organ pipe filled with a gas at 27^{o}C resonates at 400 Hz in its
fundamental mode. If it is filled with the same gas at 90^{o}C, the resonance frequency will be

Correct Answers :

[B]

Explanation :

20. A point source emits sound equally in all directions in a
nonabsorbing medium. Two points P and Q are at distances of 9 m and 25 m respectively from the source. The ratio of the
amplitudes of the waves at P and Q is

Correct Answers :

[C]

Explanation :

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