A set of 12 tuning forks is arranged in the increasing order of frequencies. Each tuning fork produces ‘y’ beats per second with previous one. The last tuning fork is an octave of the first. The fifth tuning fork has frequency 90 Hz. Find ‘y’. Hence find the frequency of the last fork.

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Solution

Let the frequency of 1st tuning fork be x.
Frequency of last tuning fork be x +11y.
8x = x + 11y
7x = 11y ---------------- (1)
Frequency of fifth tuning fork = x + 4y
90 = x + 4y --------------(2)
Using equation (1) and (2), we get:
y = 16.15 and x = 25.38

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A set of 12 tuning forks is arranged in the increasing order of frequencies. Each tuning fork produces ‘y’ beats per second with previous one. The last tuning fork is an octave of the first. The fifth tuning fork has frequency 90 Hz. Find ‘y’. Hence find the frequency of the last fork.

Let the frequency of 1st tuning fork be x. Frequency of last tuning fork be x +11y. 8x = x + 11y 7x = 11y ---------------- (1) Frequency of fifth tuning fork = x + 4y 90 = x + 4y --------------(2) Using equation (1) and (2), we get: y = 16.15 and x = 25.38

Let the frequency of 1st tuning fork be x.
Frequency of last tuning fork be x +11y.
8x = x + 11y
7x = 11y ---------------- (1)
Frequency of fifth tuning fork = x + 4y
90 = x + 4y --------------(2)
Using equation (1) and (2), we get:
y = 16.15 and x = 25.38