A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10 kg weight between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency n. The frequency n of the alternating source is :

(1) 25 Hz

(2) 50 Hz

(3) 100 Hz

(4) 200 Hz

An open pipe is in resonance in its 2^nd harmonic with tuning fork of frequency f₁. Now it is closed at one end. If the frequency of the tuning fork is increased slowly from f₁ , then again a resonance is obtained with a frequency f₂. If in this case the pipe vibrates in $n^{th}$ harmonic, then -

(1) n = 3, $f_2=\frac{3}{4}{f}_1$

(2) n = 3, $f_2=\frac{5}{4}{f}_1$

(3) n = 5, $f_2=\frac{5}{4}{f}_1$

(4) n = 5, $f_2=\frac{3}{4}{f}_1$

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

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 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

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

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)

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