JEE Main & Advanced Physics Wave Mechanics Question Bank Doppler's Effect

  • question_answer
    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) [KCET 2000; AMU 1999; Pb. PET 2003]

    A)            436 to 586                              

    B)            426 to 574

    C)            426 to 584                              

    D)            436 to 674

    Correct Answer: A

    Solution :

               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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