A cylindrical metal tube has a length of 50cm and is open at both ends. Find the frequencies between 1kHz to 2kHz at which the air column in the tube resonates. The temperature on that day is 20∘C. [Take v0=330m/s]
A
1020,11360,1700Hz
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B
1026,1368,1710Hz
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C
1328,1660,1922Hz
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D
None of these
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Solution
The correct option is B1026,1368,1710Hz As per the question we have fn=nv2L Also, v(T)=v0√1+T273 ⇒v=330√1+20273=330√293273=342ms−1 ⇒fn=342n2L=342n2×50×10−2Hz Thus, wavelengths allowed between 1000Hz and 2000Hz are for n=3,4,5, so, the values are 1026Hz,1368Hz,1710Hz.