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  4. 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 the whistle, hears frequency in the range of (speed of sound = 340 ms- 1 )

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Q. 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 the whistle, hears frequency in the range of (speed of sound = $340 \, ms^{- 1}$ )

NTA AbhyasNTA Abhyas 2020Waves

Solution:

$v_{s}=r\omega $
$v_{s}=1.2\times 2\times 3.14\times \left(\frac{400}{60}\right)=50ms^{- 1}$
$v_{min \, }=\frac{v}{v + v_{s}}\nu$
$=\frac{340}{340 + 50}\times 500=436 \, Hz \, $
$v_{max \, }=\frac{v}{v - v_{s}}v$
$=\frac{340}{340 - 50}\times 500$
$=586Hz$