Question

With neat diagram, explain various modes of vibration of a stretched string.

Answer 1

A vibration in a string is a wave. Resonancecauses a vibrating string to produce a soundwith constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos.

Answer 2

Answer:

Different modes of Vibration in stretched string:-

a) First mode of vibration:-

In this mode of vibration, the string vibration in one segment. This there are two nods at fixed ends and an antinode in between them. If ‘λ’ be the length of string and λ0 be the wave length of wave in this mode of vibration.

If ‘U’ be the velocity of wave and to be the frequency of wave in this mode of vibration

Second mode of vibration:

In this mode of vibration the string vibration in two segments. Thus there are three nodes and two antinodes between of string and l1 be the wavelength of wave in this mode of vibration.

l = λ1

If u be the velocity of wave and f1 be the frequency of wave in this mode of vibration.

This is the frequency of 1st overtone and 2nd harmonics.

Third mode of vibration:

4 nodes & 3 AN

This is the frequency of 2nd overtone or 3rd harmonics

In this way, for the 4th, 5th …… modes of vibration in the stretched string the frequency

For the fifth, 5th….. Harmonics are emitted.

The general equation of frequency of wave in stretched string is given by,

Laws of transverse vibration of a string: