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 displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities I_A/I_B is equal to :

1. 1 : 4

2. 1 : 16

3. 1 : 2

4. 1 : 1

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

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)

The diagram below shows the propagation of a wave. Which points are in the same phase :

(1) F, G

(2) C and E

(3) B and G

(4) B and F

Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2 seconds, the total energy of the pulses will be 

1. Zero

2. Purely kinetic

3. Purely potential

4. Partly kinetic and partly potential

A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

1. $\sqrt{gL}$

2. $\sqrt{gx}$

3. gL

4. gx

Two loudspeakers L₁ and L₂ driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from zero and the detector at D records a series of maxima and minima. If the speed of sound is 330 ms^–1 then the frequency at which the first maximum is observed is

(1) 165 Hz

(2) 330 Hz

(3) 496 Hz

(4) 660 Hz