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Q.

A string of musical instrument is $50 cm$ long and fundamental frequency is $270 Hz$ . If the desired frequency of $1000 Hz$ is to be produced, the required string length is

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a

$10.8 cm$

b

$5.4 cm$

c

$2.7 cm$

d

$13.5 cm$

answer is A.

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Detailed Solution

Given ,

Length $l_{1} = 50 cm$

Frequency $n_{1} = 270 Hz$

Frequency $n_{2} = 1000 Hz$

Length $l_{2} = ?$

As $n α \frac{1}{l}$

$n_{1} l_{1} = n_{2} l$

$270 \times 50 = 1000 \times l_{2}$

$∴ l_{2} = 13.5 cm$

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A string of musical instrument is 50 cm long and fundamental frequency is 270 Hz . If the desired frequency of 1000 Hz is to be produced, the required string length is