8. A tuning fork vibrating with a sonometer wire 20cm long produces 5 beats per second. Given
that the beat frequency does not change if the length of the wire is changed to 21cm, calculate
the frequency of the tuning fork and frequency of sonometer wire when changed to 21cm.

Explanation:

length of wire is proportional to frquency of sound produced by it.

n₁ /n₂ = l₂ / l₁

= 21 / 20

If n be the frequency of tuning fork

n₁ = n + 5  ;  n₂ = n - 5   ( no of beat / s  = frequency difference )

n + 5 / n - 5 = 21 / 20

20n + 100 = 21n - 105

n = 205 Hz

frequency of tuning fork = 205

the frequency of the tuning fork and frequency of sonometer wire when changed to 21cm.   = n - 5 = 200 Hz .

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