## Tuesday, January 6, 2015

### Stretched String Problems and Solutions

Problem and solution

A sonometer wire has a length of 114 cm between the two fixed ends. Where shall we place two movable bridges to divide the wire into three segments whose fundamental frequency surrender ratio of  1:3:4 ?

When the tension and linear density of the wire is kept constant, frequency of the wire is inversely proportional to its length. Taking this law into consideration the problem is solved as shown below.

Problem and solution

A wire with density and length given and extension under a load is given in the below problem.We need to calculate the frequency of the wire under fundamental mode using the formula for the frequency of a stretched string.

This problem  is based on law of tension.When frequency is changed its tension will change as shown below.

Frequency of the tuning fork is directly proportional to thickness of the fork, velocity of the wave and inversely proportional to Squire of its length.

Speed of a longitudinal wave in a medium

The velocity of a wave in a medium can be expressed as the ratio of Squire root of  modulus of elasticity of the medium to the density of the medium. It is assumed that the propagation of the sound happens in a isothermal way. Anyway practically it is found that the temperature of the particles of the medium is not going to remain constant during the propagation of the wave. It is rather in adiabatic process when the heat energy of the system remains constant but the temperature increases.

It can be further proved that velocity of sound is independent of pressure.When ever pressure changes its volume also changes which generates same change in density and hence the ratio of pressure to density remain constant.

we can further compare this velocity with RMS velocity of a gas as shown below.Both of them depend on the absolute temperature similarly.

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