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Mechanical Properties Of Fluids

Question
CBSEENPH11020646

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 strings is

  • 155 Hz

  • 205 Hz

  • 10.5 Hz

  • 105 Hz

Solution

D.

105 Hz

Given l = 75 cm, f1 = 420 Hz and f2 = 315 Hz
As two consecutive resonant frequencies for a string fixed at both ends will be +
straight f subscript 1 space equals space fraction numerator nv over denominator 2 l end fraction space and space straight f subscript 2 space equals fraction numerator left parenthesis straight n plus 1 right parenthesis over denominator 2 straight R end fraction

rightwards double arrow space straight f subscript 2 minus straight f subscript 1 equals space 420 space minus space 315 space

rightwards double arrow space fraction numerator left parenthesis straight n plus 1 right parenthesis straight v over denominator 2 l end fraction space minus fraction numerator nv over denominator 2 space l end fraction space equals space 105 space Hz

rightwards double arrow space fraction numerator straight v over denominator 2 space l end fraction space equals space 105 space Hz
Thus, lowest resonant frequency of a string is 105 Hz.