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An observer A located at a distance r(A)...

An observer `A` located at a distance `r_(A)=5.0 m ` from a ringing tuning fork notes the sound to fade away `tau =19 s ` later than an observer `B` who is located at a distance `r_(B)=50m` from the tuning fork. Find the damping coefficient `beta` of oscillations of the tuning fork. The sound velocity `v=340 m//s`.

Text Solution

Verified by Experts

We treat the fork as a point source. In the absenece of damping the oscillation has the form
`(Const. )/(r) cos (omegat-kr)`
Because of the fork the amplitude of oscillation decreases exponentially with the retarted tme `(i.e.` the time at which the wave started from the source.`)` Thus we write for the wave amplitude.
`xi=(Const. ) /(r)e^(-beta(t-(r)/(v)))`
Thus means that `(e^(-beta(t + tau-(r_(A))/(v))))/( r_(A))=(e^(-beta(t+tau-(r_(B))/( v))))/( r_(B))`
Thus `e^(-beta(tau+(r_(B)-r_(A))/( v)))=(r_(A))/( r_(B))` or `beta=(1n(r_(B))/(r_(A)))/(tau+(r_(B)-r_(A))/(v))=0.12.s^(-1)`
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Knowledge Check

  • A vibrating tuning fork is moving slowly and uniformly ins a horizontal circular path of radiu 8 m . The shortest distance of an observer ins ame plane from the tuning fork is 9m. The distance between the tuning fork and observer at the instant when apparent frequency becomes maximum is

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