Question

In: Physics

(a)Find the frequencies of the fundamental, 1st and 2nd overtones of a 1.00m wire whose wave...

(a)Find the frequencies of the fundamental, 1st and 2nd overtones of a 1.00m wire whose wave speed is 200m/s. (b) Find the wavelengths of the sound waves created by the vibrating wire for all three modes (speed of sound is 345m/s).

Also, why is wave speed from (a) different from the speed of sound?

Solutions

Expert Solution

a)

The fundamental frequency of a vibrating string of length L is given by

where v is the speed of the wave in the sting.

The frequency of nth overtone is given by

where n=1,2,3,4..................

here

v=200m/s

L=1.00m

so, The fundamental frequency of a vibrating string of length L=1.00m is given by

The frequency of 1st overtone is given by

The frequency of 2nd overtone is given by

b)

we know that the length of the sound is given by

here

v=345m/s

so the wavelength of the sound waves created by the vibrating wire for fundamental mode is given by

the wavelength of the sound waves created by the vibrating wire for 1st overtone is given by

the wavelength of the sound waves created by the vibrating wire for 2nd overtone is given by

NOTE:

the speed of sound v

where

Ks is a coefficient of stiffness, the isentropic bulk modulus and is the density.

the sound is propagated through the air and the wave is propagated through the wire. the coefficient of stiffness and density are different for air and wire.hence the speed of the wave and the speed of the sound is different.


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