A certain string will resonate to several frequencies, the lowest of which is 200 cps. What are the next three higher frequencies to which it resonates?

(1) 400, 600, 800

(2) 300, 400, 500

(3) 100, 150, 200

(4) 200, 250, 300

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