A whistle of frequency $500 Hz$ tied to the end of a string of length $1.2 m$ revolves at $400 \,rev/min$. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range (speed of sound $= 340 m/s$)
Diffcult
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(a) The linear velocity of Whistle
${v_S} = r\omega = 1.2 \times 2\pi \frac{{400}}{{60}} = 50\,m/s$
When Whistle approaches the listener, heard frequency will be maximum and when listener recedes away, heard frequency will be minimum
So, ${n_{\max }} = n\,\left( {\frac{v}{{v - {v_s}}}} \right) = 500\,\left( {\frac{{340}}{{290}}} \right) = 586Hz$
${n_{\min }} = \,n\,\left( {\frac{v}{{v + {v_s}}}} \right) = 500\,\left( {\frac{{340}}{{390}}} \right) = 436Hz$
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