A) \[300\,\,Hz\]
B) \[350\,\,Hz\]
C) \[375\,\,Hz\]
D) \[415\,\,Hz\]
Correct Answer: D
Solution :
Key Idea: When length of air column is\[\frac{\lambda }{4}\], then first resonance occurs. If we adjust the length of air-column in closed organ pipe as such its any natural frequency equals to the frequency of tuning fork, then the amplitude of forced vibrations of air-column increases very much. This is the state of resonance. At first resonance \[l=\frac{\lambda }{4}\] So, frequency of tuning fork \[f=\frac{v}{\lambda }=\frac{v}{4l}\] Given,\[l=20\,\,cm=0.2\,\,m,\,\,v=332\,\,m/s\] Hence,\[f=\frac{332}{4\times 0.2}=415\,\,Hz\]
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