A string is rigidly tied at two ends and its equation of vibration is given by $y=\left(\cos 2\mathrm{\pi }t \right)\left(\sin 2\mathrm{\pi }x\right)$Then minimum length of the string is :

1. 1 m

2. $\frac{1}{2}m$

3. 5 m

4. 2π m

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :

(1) 163.84 Hz

(2) 400 Hz

(3) 320 Hz

(4) 204.8 Hz

An empty vessel is getting filled with water, then the frequency of vibration of the air column in the vessel 

(1) Remains the same

(2) Decreases

(3) Increases

(4) First increases then decrease

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude ${\rho }_0$ inside the tube. If the atmospheric pressure is ${\rho }_A$ , then the ratio of maximum and minimum pressure at the closed end of the tube will be :

1. $\frac{({\rho }_A+{\rho }_0)}{({\rho }_A-{\rho }_0)}$

2. $\frac{({\rho }_A+2{\rho }_0)}{({\rho }_A-2{\rho }_0)}$

3. $\frac{{\rho }_A}{{\rho }_A}$

4. $\frac{\left({\rho }_A+\frac{1}{2}{\rho }_0\right)}{\left({\rho }_A-\frac{1}{2}{\rho }_0\right)}$

An open pipe of length l vibrates in the fundamental mode. The pressure variation is maximum at :

(1) 1/4 from ends

(2) The middle of the pipe

(3) The ends of the pipe

(4) At 1/8 from ends of pipe middle of the pipe

In a closed organ pipe, the frequency of the fundamental note is 50 Hz. The note of which of the following frequencies will not be emitted by it :

(1) 50 Hz

(2) 100 Hz

(3) 150 Hz

(4) None of the above

The frequency of a whistle of an engine is 600 cycles/sec is moving with the speed of 30 m/sec towards an observer. The apparent frequency will be (velocity of sound = 330 m/s) [MP PMT 1989]

(1) 600 cps

(2) 660 cps

(3) 990 cps

(4) 330 cps

A source of sound is travelling with a velocity 40 km/hour towards the observer and emits the sound of frequency 2000 Hz. If the velocity of sound is 1220 km/hour, then what is the apparent frequency heard by an observer 

(1) 2210 Hz

(2) 1920 Hz

(3) 2068 Hz

(4) 2086 Hz

A source of sound and listener are approaching each other with a speed of 40 m/s. The apparent frequency of note produced by the source is 400 cps. Then, its true frequency (in cps) is (velocity of sound in air = 360 m/s) 

(1) 420

(2) 360

(3) 400

(4) 320

A man sitting on a moving train hears the whistle of the engine. If the frequency of the whistle is 600 Hz, then:

1. the apparent frequency as heard by him is smaller than 600 Hz.

2. the apparent frequency is larger than 600 Hz.

3. the frequency as heard by him is 600 Hz.

4. None of the above