A) 255m/s
B) 250 m/s
C) 350 m/s
D) none of these
Correct Answer: A
Solution :
Here: Length of first pipe \[{{l}_{1}}=25\text{ }cm\] Length of second pipe\[{{l}_{2}}=25.5\text{ }cm\] Frequency/beat = 0.1 beat/sec Frequence of first pipe\[{{f}_{1}}\] is given by, \[\frac{\upsilon }{2{{l}_{1}}}=\frac{\upsilon }{2\times 25}=\frac{\upsilon }{50}Hz\] Frequency of second pipe\[{{f}_{2}}\]is given by, \[\frac{\upsilon }{2{{l}_{2}}}=\frac{\upsilon }{2\times 25.5}=\frac{\upsilon }{51}Hz\] (where\[\upsilon \]is velocity of sound) Hence, the frequency \[f={{f}_{1}}-{{f}_{2}}\] \[0.1=\frac{\upsilon }{50}-\frac{\upsilon }{51}=\frac{\upsilon }{50\times 51}\] Or \[\upsilon =0.1\times 50\times 51\] \[\upsilon =255\text{ }m/s\]
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