Question

A tuning fork gives 5 beats/s, when sounded
together with a sonometer wire having separation
between bridges 20 cm. It again gives 5 beats/s
when separation between bridges increased to
21 cm. The frequency of tuning fork is
(1) 200 Hz
(2) 205 Hz
(3) 210 Hz
(4) 195 Hz​

Answer 1

The frequency of tuning fork is 205 Hz.

Explanation:

n + 5 = 1 / 2 x 20 √ T / m ------ (1)

And

n - 5 = 1 / 2 x 21 √ T / m   -------(2)

Dividing equation (1) by (2) we get

n + 5 / n - 5 = 21 / 20

20 ( n + 5 ) = 21 ( n - 5)

20 n + 100 = 21 n - 105

100 + 105 = 21n - 20 n

n = 205 Hz

Hence the frequency of tuning fork is 205 Hz.

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A tuning fork of frequency 280 Hz produces 10 beats per second when sounded with a vibrating sono-meter string . when the tension in the string increase slightly , it produces 11 beats per sec. the original frequency of the vibrating sono-meter is ????

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