Question

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the wavelength of the sound it will produce?

Answer 1

Answer:

wavelength = 0.8989 m

Explanation:

Given data:

weight of wire is 8.25 g

length of wire is 65 cm

speed of sound in room is 344 m/s

time of returning of pulse is 7.84 ms

There are three time period

Time period $= \frac{7.84\times 10^{-3}}{3} = 2.6133\times 10^{-3} s$

$frequency = \frac{1}{T}$

                  $=\frac{ 1}{2.6133\times 10^{-3})} = 382.6579 Hz$

velocity = wavelength × frequency

wavelength $= \frac{velocity}{frequency}$

                   $= \frac{344}{382.6579}$

wavelength = 0.8989 m