Question

A sonometer wire under tension of 64 Newton vibrating in its fundamental mode is in resonance with a vibrating tuning fork. The vibrating portion of the sonometer wire has a length of 10 cm and a mass of one gm. The vibrating tuning fork is now moved away from the vibrating wire with a constant speed and an observer standing near sonometer hears one beat per second. Calculate the speed with which the tuning fork is moved, if the velocity of sound in air is 300 m s^–1.

Answer 1

The fundamental frequency of the sonometer wire is

Actual frequency of the vibrating tuning fork = f = 400 Hz. The apparent frequency of the tuning fork is 

where v = velocity of sound in air = 300 m s^–1.

 v_s = velocity of the tuning fork, which is moving away from the vibrating wire.