A) \[256\times \frac{330}{325}-256\]
B) \[256-\frac{256\times 330}{335}\]
C) \[\frac{256\times 330}{325}-\frac{256\times 330}{325}\]
D) \[256\times \frac{335}{325}-256\]
Correct Answer: D
Solution :
In this case, the observer moves with the source. For direct sound, the velocity of source is the same as that of observer. The apparent frequency n is given by \[n=n\left( \frac{v-{{v}_{0}}}{v-{{v}_{s}}} \right)\] As \[{{v}_{0}}={{v}_{s}}\] \[\therefore \] \[n=n=256\,Hz\] For the reflected sound, the apparent frequency n is given by \[n=n\left( \frac{v-{{v}_{0}}}{v-{{v}_{s}}} \right)\] Here, \[n=256\,Hz,\,v=330\,m/s\] Also, the observer moves in opposite direction to the source, so \[{{v}_{o}}=-5\,m/s\] and \[{{v}_{s}}=+5\,m/s\] \[\therefore \] \[n=256\left( \frac{330-(-5)}{330-(5)} \right)\] \[=256\times \frac{335}{225}\] Hence, beats per second \[=n-n\] \[=256\times \frac{335}{325}-256\]
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