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

(1) 436 to 586

(2) 426 to 574

(3) 426 to 584

(4) 436 to 674

(1) The linear velocity of Whistle

${v}_{S}=r\omega =1.2×2\pi \frac{400}{60}=50\text{\hspace{0.17em}}m/s$

When Whistle approaches the listener, heard frequency will be maximum and when listener recedes away, heard frequency will be minimum

So, ${n}_{\mathrm{max}}=n\text{\hspace{0.17em}}\left(\frac{v}{v-{v}_{s}}\right)=500\text{\hspace{0.17em}}\left(\frac{340}{290}\right)=586Hz$

${n}_{\mathrm{min}}=\text{\hspace{0.17em}}n\text{\hspace{0.17em}}\left(\frac{v}{v+{v}_{s}}\right)=500\text{\hspace{0.17em}}\left(\frac{340}{390}\right)=436Hz$

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