Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the lower frequency in the setting is 360 Hz. the beat frequency when the two wires are sounded together is :

(1) 5

(2) 8

(3) 6

(4) 10

The first overtone of a stretched wire of given length is 320 Hz. The first harmonic is : 

(1) 320 Hz

(2) 160 Hz

(3) 480 Hz

(4) 640 Hz

The sound carried by the air from a sitar to a listener is a wave of the following type :

(1) Longitudinal stationery

(2) Transverse progressive

(3) Transverse stationery

(4) Longitudinal progressive

Three similar wires of frequency n₁, n₂ and n₃ are joined to make one wire. Its frequency will be :

(1) $n=n_1+n_2+n_3$

(2) $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

(3) $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$

(4) $\frac{1}{n^1}=\frac{1}{n_1^2}+\frac{1}{n_2^2}+\frac{1}{n_3^2}$

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n₁ and the other with frequency n₂. The ratio n₁/n₂ is given by :

(1) 2

(2) 4

(3) 8

(4) 1

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