A sonometer wire under tension of 64 N 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 mass of 1 g. The vibrating tuning fork is now moved away from the vibrating wire with a constant speed and an observer standing near the sonometer hears one beat per second. Calculate the speed with which the tuning fork is moved, if the speed of sound in air is 300 m/s.

Explanation

Fundamental freqency of sonometer wire,
`f = (upsilon)/(2l)= (1)/(2l)sqrt((T)/(mu))`
= `(1)/(2xx0.1) sqrt((64xx0.1)/(10_(-3))`
= `400 H_(Z)`
Given `f_(b) = f - f' = 1 H_(Z)`
`:. f' =399 H_(Z)`
Using `f' =f((upsilon)/(upsilon + upsilon_(s)))`
or `399 = 400 ((300)/(300 + upsilon_(s)))`
Solving we get, `upsilon_(s) = 0.75 m//s`