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Question

A sonometer wire 110 cm long produces a resonance with a tuning fork. When its length is decreased by 10 cm, 9 beats per second are heard. The frequency of tuning fork is __________.

A
90 Hz
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B
85 Hz
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C
82 Hz
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D
75 Hz
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Solution

The correct option is D 90 Hz
We know that for a sonometer wire frequency is inversely proportional to length of sonometer wire.
Let the frequency of tuning fork be f.
This is in resonance with a sonometer wire of length 110cm
So, f=k110
When the length of the wire is decreased by 10 cm, new length of the wire l=11010=100 cm
Frequency changes to f=k100
It is given that beats with a frequency of 9Hz are formed i.e. ff=9
Therefore, 9=k100k110
k=9×1100
So, f=9×1100110=90Hz

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