question_answer

An observer is standing 500 m away from a vertical hill. Starring from a point between the observer and die hill, a police van moves towards hill with uniform speed sounding a siren of frequency of 1000 Hz. If the  frequency of the sound heard by the observer directly from the siren is 970 Hz, the frequency of the sound heard by the observer after reflection from the hill (Hz) is nearly (Velocity of sound in air\[=300m{{s}^{-1}}\])

A)  1042                                     

B)  1031

C)  1022                                     

D)  1012

Correct Answer: B

Solution :

  Let the velocity of siren-source is \[{{v}_{s}}.\] Van goes away from observer and towards to  hill. Given that n = 1000 Hz (actual frequency) Let n is apparent frequency for observer in  first condition. \[n=970Hz\] (apparent frequency) \[\therefore \]                  \[n=n\left( \frac{v}{v+{{v}_{s}}} \right)\] or            \[970=1000\left( \frac{330}{330+{{v}_{s}}} \right)\] \[(330+{{v}_{s}})=\frac{330}{97}\times 100\] \[{{v}_{s}}=\frac{330\times 3}{97}\] For second condition, when sound reflects from the hill and approaches the observer, \[n=n\left( \frac{v}{v-{{v}_{s}}} \right)\] \[n=1000\left( \frac{330}{330-\frac{330\times 3}{97}} \right)\] \[=1000\left( \frac{330\times 97}{330(97-3)} \right)\] \[=1000\left( \frac{97}{94} \right)\] \[=500\left( \frac{97}{47} \right)\] \[=1031\,Hz\]