Question

A given length of a sonometer wire is in resonance with tuning fork.if length the wire is reduced by 4% the wire vibrating with the fork produces 5 beats per second what is the frequency of tuning fork

Answer 1

Answer: 245 Hz

Explanation:see attachment..

Answer 2

The frequency of tuning fork is 243 Hz.

Explanation:

Given that,

Number of beat = 5

We need to calculate the frequency of tuning fork

Using formula of frequency

$n=\dfrac{p}{2}\sqrt{\dfrac{T}{Ml}}$

$n\propto\sqrt{\dfrac{1}{l}}$

Frequency of sonometer wire = frequency of tuning fork energy

$n_{s}=n_{t}$

If length the wire is reduced by 4% the wire.

$l'=l-\dfrac{4}{100}l$

$l'=l-0.04l$

$l'=0.96l$

We need to calculate the frequency when length the wire is reduced

$n'_{s}=\dfrac{p}{2}\sqrt{\dfrac{T}{Ml}}$

Where, p = number of loop

T = tension

M = mass

Put the value into the formula

$n'_{s}=\dfrac{p}{2}\sqrt{\dfrac{T}{M\times0.96l}}$

$n'_{s}=\dfrac{1}{\sqrt{0.96}}\dfrac{p}{2}\sqrt{\dfrac{T}{M l}}$

$n'_{s}=1.02n$

Now, using formula of beat frequency

$n'_{s}-n=n_{b}$

Put the value into the formula

$1.0206n-n=5$

$n=\dfrac{5}{0.0206}$

$n=243\ Hz$

Hence, The frequency of tuning fork is 243 Hz.

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Topic : frequency

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