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, \[n=n\left( \frac{v}{v-{{v}_{s}}} \right)\] \[n=1000\left( \frac{330}{330-\frac{330\times 3}{97}} \right)\] \[=1000\left( \frac{330\times 97}{330(97-3)} \right)\] \[=1000\left( \frac{97}{94} \right)\] \[=500\left( \frac{97}{47} \right)\] \[=1031\,Hz\]You need to login to perform this action.
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