In: Physics
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.