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?

10 cm

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15 cm

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18 cm

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20 cm

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Solution

The correct option is D
20 cm

Let initial frequency, $f_{1} = 256 H z$

Final frequency, $f_{2} = 1024 H z$

Initial length of the wire, $l_{1} = 80 c m$

Final length of the wire, $l_{2} = ?$
The frequency of sound produced by a stretched wire under same tension
$F \propto \frac{1}{l}$
or, $f l = c o n s t a n t$
$∴ f_{1} l_{1} = f_{2} l_{2}$
or, $l_{2} = \frac{f_{1} \times l_{1}}{f_{2}} = \frac{256 \times 80}{1024} = 20 c m$

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