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Question

A wire of length 80 cm under some tension produces a sound of frequency 256 Hz. What length of wire will produce the sound of frequency 1024 Hz under the same tension?


  1. 18 cm
     

  2. 20 cm

  3. 15 cm
     

  4. 10 cm
     


Solution

The correct option is B

20 cm


Let initial frequency,f1=256 Hz

      Final frequency, f2=1024 Hz

      Initial length of the wire, l1=80 cm

      Final length of the wire, l2=?
The frequency of sound produced by a stretched wire under same tension
F1l
or, fl = constant
f1l1=f2l2
or, l2=f1×l1f2=256×801024=20 cm

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