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A sonometer wire under tension of 64 N u...

A sonometer wire under tension of `64 N` uibrating in its fundamental mode is in resonance with a uibrating tuning fork . The uibrating portion of the sonemether wire has a length of `10 cm` and mass of `1 g` . The uibrating tuning fork is now moved away from the uibrating 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 speed of sound in air is `300 m//s` .

Text Solution

Verified by Experts

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`
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