A set of 8 tuning forks is arranged in a series of increasing order of frequencies. Each fork gives 4 beats per second with the next one and the frequency of last fork is twice that of the first . Calculate the frequencies of the first and the last fork
Answers
Given info : A set of 8 tuning forks is arranged in a series of increasing order of frequencies. Each fork gives 4 beats per second with the next one and the frequency of last fork is twice that of the first.
To find : The frequencies of the first and the last fork.
solution : let n1 , n2 , n3 .... n8 are frequencies of all 8 tunning fork.
a/c to question,
n2 = n1 + 4
= n1 + 1 × 4
n3 = n2 + 4 = n1 + 4 + 4
= n1 + 2 × 4
n4 = n3 + 4 = n1 + 2 × 4 + 4
= n1 + 3 × 4
so on ...
n8 = n1 + 7 × 4 ......(1)
but also given, n8 = 2n1 .....(2)
from equations (1) and (2) we get,
2n1 = n1 + 28
⇒n1 = 28 Hz
and n8 = 2n1 = 56 Hz
Therefore the frequencies of the first and the last forks are 28Hz and 56 Hz respectively.
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