Question

One string of a certain musical instrument is 75.0-cm-long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s.

(a) To what tension force must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that the breaking stress of the wire is very large and isn’t exceeded.)

(b) What frequency sound does this string produce in its fundamental mode of vibration?

Answer 1

linear mass density

l is the length of wire.

so first the frequancy of second overtone is,

where is the wavelength of second overtone and v is the velocity of sound so putting values we get,

f=449.67 Hz

or frequancy is also given by,

,

solving of tension

putting all values we get,

T= 590.3N

2) frequancy of fundamental mode of vibration

putting all values we get frequancy

f= 149.9 Hz