A wave motion has the function $y=a_0\sin (\omega t-kx)$. The graph in figure shows how the displacement y at a fixed point varies with time t. Which one of the labeled points shows a displacement equal to that at the position $x=\frac{\pi }{2k}$ at time t = 0

(1) P

(2) Q

(3) R

(4) S

If the speed of the wave shown in the figure is 330m/s in the given medium, then the equation of the wave propagating in the positive x-direction will be (all quantities are in M.K.S. units) :

(1) $y=0.05\sin 2\pi (4000t-12.5x)$

(2) $y=0.05\sin 2\pi (4000t-122.5x)$

(3) $y=0.05\sin 2\pi (3300t-10x)$

(4) $y=0.05\sin 2\pi (3300x-10t)$

The correct graph between the frequency n and square root of density (ρ) of wire, keeping its length, radius and tension constant, is :

(1)

(2)

(3)

(4)

An organ pipe is closed at one end has a fundamental frequency of 1500 Hz. The maximum number of overtones generated by this pipe which a normal person can hear is : 

(1) 14

(2) 13

(3) 6

(4) 9

The equation of displacement of two waves are given as $y_1=10\sin \left(3\pi t+\frac{{\displaystyle \pi }}{{\displaystyle 3}}\right)$; $y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)$. Then what is the ratio of their amplitudes ?

1. 1 : 2

2. 2 : 1

3. 1 : 1

4. None of these

A police car moving at 22 m/s, chases a motorcyclist. The policeman sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats 

(1) 33 m/s

(2) 22 m/s

(3) Zero

(4) 11 m/s

The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of the source. If the velocity of sound in air is 300 m/sec, the velocity of the source is : (It is given that velocity of source << velocity of sound) 

(1) 6 m/sec

(2) 3 m/sec

(3) 1.5 m/sec

(4) 12 m/sec

The ends of a stretched wire of length L are fixed at x = 0 and x = L. In one experiment, the displacement of the wire is $y_1=A\sin (\pi x/L)\sin \omega t$ and energy is E₁, and in another experiment its displacement is $y_2=A\sin (2\pi x/L)\sin 2\omega t$ and energy is E₂. Then :

(1) E₂ = E₁

(2) E₂ = 2E₁

(3) E₂ = 4E₁

(4) E₂ = 16E₁

Two waves having sinusoidal waveforms have different wavelengths and different amplitudes. They will be having :

(1) Same pitch and different intensity

(2) Same quality and different intensity

(3) Different quality and different intensity

(4) Same quality and different pitch

A source emits a sound of frequency of 400 Hz, but the listener hears it to be 390 Hz. Then 

(1) The listener is moving towards the source

(2) The source is moving towards the listener

(3) The listener is moving away from the source

(4) The listener has a defective ear