A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz then the waves would travel on its with a velocity of :

(1) 125 m/s

(2) 250 m/s

(3) 500 m/s

(4) 1000 m/s

The fundamental frequency of a sonometre wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be :

(1) n

(2) $\frac{n}{\sqrt{2}}$

(3) $\frac{n}{2}$

(4) $\frac{n}{2\sqrt{2}}$

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

The length of two open organ pipes are l and $(l+\Delta l)$ respectively. Neglecting end correction, the frequency of beats between them will be approximate :

(1) $\frac{v}{2l}$

(2) $\frac{v}{4l}$

(3) $\frac{v\Delta l}{2l^2}$

(4) $\frac{v\Delta l}{l}$

(Here v is the speed of sound)

A tube closed at one end and containing air is excited. It produces the fundamental note of frequency of 512 Hz. If the same tube is open at both the ends the fundamental frequency that can be produced is :

(1) 1024 Hz

(2) 512 Hz

(3) 256 Hz

(4) 128 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

If the velocity of sound in air is 350 m/s. Then the fundamental frequency of an open organ pipe of length 50 cm, will be

(1) 350 Hz

(2) 175 Hz

(3) 900 Hz

(4) 750 Hz

The fundamental note produced by a closed organ pipe is of frequency f. The fundamental note produced by an open organ pipe of same length will be of frequency

(1) $\frac{f}{2}$

(2) f

(3) 2f

(4) 4f

If the velocity of sound in air is 336 m/s. The maximum length of a closed pipe that would produce a just audible sound will be : 

(1) 3.2 cm

(2) 4.2 m

(3) 4.2 cm

(4) 3.2 m