The length of a sonometer wire is 0.75 m and density 9 x 10³ Kg/m³. It can bear the stress of 8.1 x 10⁸ N/m² without exceeding the elastic limit. The fundamental frequency that can be produced in the wire is:

(1) 200 Hz

(2) 150 Hz

(3) 600 Hz

(4) 450 Hz

The string of a violin has a frequency of 440 cps. If the violin string is shortened by one fifth, its frequency will be changed to:

(1) 440 cps

(2) 880 cps

(3) 550 cps

(4) 2200 cps

A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 256 Hz. When the tension is increased by 1 kg-wt, the frequency of the fundamental node increases to 320 Hz. The initial tension is:

(1) 3/4 kg wt

(2) 4/3 kg wt

(3) 16/9 kg wt

(4) 20/9 kg wt

In the case of a closed pipe which harmonic the p^th overtone will be:

(1) 2p + 1

(2) 2p -1

(3) p + 1

(4) p - 1

The pitch of an organ pipe is highest when the pipe is filled with:

(1) Air

(2) Hydrogen

(3) Oxygen

(4) Carbon dioxide

A cylindrical tube, open at both ends, has a fundamental frequency f in the air. The tube is dipped vertically in water so that half of it is in the water. The fundamental frequency of the air column is now:

(1) $\frac{f}{2}$

(2) $\frac{3f}{4}$

(3) f

(4) 2f

For a certain organ pipe, three successive resonance frequencies are observed at 425, 595, and 765 Hz respectively. Taking the speed of sound in air to be 340 m/s, the fundamental frequency of the pipe (in Hz) is:

(1) 425

(2) 170

(3) 85

(4) 245

A closed pipe of length 10 cm has its fundamental frequency equal to half of that of the second overtone of an open pipe. The length of the open pipe:

(1) 10 cm

(2) 20 cm

(3) 30 cm

(4) 40 cm

The vibrations of four air columns under identical conditions are represented in the figure below. The ratio of frequencies $n_p : n_q : n_r : n_s$ will be:

(1) 12: 6: 3: 4

(2) 1: 2: 4: 3

(3) 4: 2: 3: 1

(4) 6: 2: 3: 4

In the resonance tube, two successive positions of resonance are obtained at 15 cm and 48 cm. If the frequency of the fork is 500 cps, the velocity of sound is:

(1) 330 m/s

(2) 300 m/s

(3) 1000 m/s

(4) 360 m/s