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  4. A fork A has frequency 2% more than the standard fork and B has a frequency 3% less than the frequency of same standard fork. The forks A and B when sounded together produced 6 beats/s. The frequency of fork A is

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Q. A fork A has frequency 2% more than the standard fork and B has a frequency 3% less than the frequency of same standard fork. The forks A and B when sounded together produced 6 beats/s. The frequency of fork A is

Electromagnetic Waves

Solution:

The frequency of A
$ n_A = n + \frac{2}{100} n$
and the frequency of B
$ n_B = n - \frac{3}{100} n$
According to question
$ n_A - n_B = 6$
$ \big(n + \frac{2}{100}n \big) - \big(n - \frac{3}{100}n \big) = 6$
or $ \frac{5}{100}n = 6$
$\Rightarrow n = \frac{600}{5} = 120 Hz$
The frequency of A
$ n_A = \big(n + \frac{2}{100}n \big) = 120 + \frac{2}{100} \times 120$
$ = 122.4 \, Hz$