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

10cm

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15cm

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18cm

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20cm

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Solution

The correct option is D
20cm

$f_{1} = 256 H z f_{2} = 1024 H z l_{1} = 80 c m$
The frequency of sound produced by a stretched wire
$F \propto \frac{1}{l}$
$\Rightarrow f l =$ constant
$∴ f_{1} l_{1} = f_{2} l_{2}$
$\Rightarrow l_{2} = \frac{f_{1} l_{1}}{f_{2}} = \frac{256 \times 80}{1024} = 20 c m$

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

The correct option is D 20cm f1=256 Hzf2=1024 Hzl1=80 cm The frequency of sound produced by a stretched wire F∝1l ⇒fl= constant ∴f1l1=f2l2 ⇒l2=f1l1f2=256×801024=20cm