Question

77. Two tuning forks x and y produce tones of
frequencies 256 Hz and 262 Hz respectively. An
unknown tone sounded with x produces, beats.
When it is sounded with y the number of beats
produced is doubled. The unknown frequency is
1) 254Hz 2) 258Hz 3) 264Hz 4) 259Hz​

Answer 1

The unknown frequency is 258 Hz.

Explanation:

Frequency "f" = | 256 - f|

                      = | 262 - f|

| 262 - f| = | 256 - f| x 2

262 - f = ± ( 2 x 256 - 2 x f)

First case:

262 - f =  512 - 2f

2f - f = 512 - 262

f = 250 Hz

Second case:

262 - f =   - 512 + 2f

3f = 774

f = 774/3

f = 258

Unknown frequency can not be greater than 262 Hz because no. of beats heard with 262 Hz is more then the no. beats heard with 256 Hz .

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