# A set of 28 tuning forks is arranged in a series of decreasing frequencies. The first tuning fork is higher ocatve of last tuning fork. When the two consecutive tuning forks are sound together, 4 beats are produced. Find the frequency of first and last tuning fork.

### Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Let the frequency of last tuning fork is v. Thus the frequency of first tuning fork will be 2v. As the two successive tuning forks produce 4 beats, therefore the frequency of other tuning fork will be

2v, 2v-4, 2v-8.........................v.

The above series is AP series. For AP series we have

T_{n }= a + (n-1)d

Here T_{n} = v, a = 2v,

n = 28, d = -4

Therefore, v = 2v + (28 - 1) (-4)

or v = 108 Hz and 2v = 216 Hz

### Answered by | 4th Jun, 2014, 03:23: PM

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