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Question

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is
  1. 305 Hz
  2. 105 Hz
  3. 205 Hz
  4. 10.5 Hz


Solution

The correct option is B 105 Hz
Frequency : f=v2Ln, where v is the velocity of sound, n is an integer and f is the frequency.
The highest common factor will be the fundamental frequency.
HCF of 420 and 315 is 105.
Hence, the resonant frequency is 105 Hz.
 

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