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Question

A string in a musical instrument is $$50 cm$$ long and its fundamental frequency is $$800 Hz$$. If a frequency of $$1000 Hz$$ is to be produced, then required length of string is


A
37.5cm
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B
40cm
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C
50cm
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D
62.5cm
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Solution

The correct option is A $$40 cm$$
We know that for frequency of sound in string the formula is, $$\displaystyle v = \frac {1}{2l}\sqrt {\frac {T}{m}}$$ or $$\displaystyle v\ \alpha \ \frac {1}{l}$$
$$\displaystyle \dfrac {v_1}{v_2} = \dfrac {l_2}{l_1}\Rightarrow \dfrac {800}{1000} = \dfrac {l_2}{50}$$
$$\displaystyle l_2 = 50 \times \dfrac {800}{1000}=40 cm$$

Physics

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