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 motorcyclist does not observe any beats.
(Speed of sound=330 m/s) 

(1) 33 m/s

(2) 22 m/s

(3) Zero

(4) 11 m/s

An observer moves towards a stationary source of sound with a speed 1/5^th of the speed of sound. The wavelength and frequency of the sound emitted are λ and f respectively. The apparent frequency and wavelength recorded by the observer are respectively :

1. $1.2f, \lambda$

2. $f,1.2\lambda$

3. $0.8f,0.8\lambda$

4. $1.2f,1.2\lambda$

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

Consider ten identical sources of sound all giving the same frequency but having phase angles which are random. If the average intensity of each source is I₀, the average of resultant intensity I due to all these ten sources will be :

(1) I = 100 I₀

(2) I = 10 I₀

(3) I = I₀

(4) $I=\sqrt{10}{I}_0$

41 forks are so arranged that each produces 5 beats per sec when sounded with its near fork. If the frequency of the last fork is double the frequency of the first fork, then the frequencies of the first and last fork are respectively :

(1) 200, 400

(2) 205, 410

(3) 195, 390

(4) 100, 200

Two identical wires have the same fundamental frequency of 400 Hz when kept under the same tension. If the tension in one wire is increased by 2%, the number of beats produced will be :

1. 4

2. 2

3. 8

4. 1

16 tunning forks are arranged in the order of increasing frequencies. Any two successive forks give 8 beats per sec when sounded together. If the frequency of the last fork is twice the first, then the frequency of the first fork is 

(1) 120

(2) 160

(3) 180

(4) 220

The frequency of a stretched uniform wire under tension is in resonance with the fundamental frequency of a closed tube. If the tension in the wire is increased by 8 N, it is in resonance with the first overtone of the closed tube. The initial tension in the wire is 

(1) 1 N

(2) 4 N

(3) 8 N

(4) 16 N

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, $f_2=\frac{3}{4}{f}_1$