Question

A tuning fork whose natural frequency is 440 Hz is placed just above the open end of a tube that contains water. The water is slowly drained from the tube while the tuning fork remains in place and is kept vibrating. The sound is found to be enhanced when the air column is 60 cm long and when it is 100 cm long. Find the speed of sound in air in m/s.

Answer 1

The sound is enhanced (i.e constructive interference occurs) when the air column is $60cm$ and $100cm$ long.
Increment in the air column length $\Delta l=100-60=40cm=0.4m$
This length must be equal to half of wavelength.
$\therefore$ $\Delta l=\frac{\lambda }{2}$
$\therefore$ $\lambda =2\Delta l=2\times 0.4=0.8m$
So, velocity of sound $v=\nu \lambda$
$v=440\times 0.8=352m/s$