A tuning fork with a frequency of 336 Hz and a tuning fork of unknown frequency

Question

A tuning fork with a frequency of 336 Hz and a tuning fork of unknown frequency produce beats with a frequency of 5.5 when struck at the same time. A small piece of putty is placed on the tuning fork with the known frequency and it's frequency is lowered slightly. When struck at the same time, the two forks now produce a beat frequency of 7.5 Hz.

1) What is frequency of tuning fork which originally had a frequency of 336 Hz after the putty has been placed on it? f1= ____ Hz

2) What is frequency of the second turning fork? f2= ____ Hz

Explanation / Answer

The beat frequency fb is produced as a result of destructive interference between waves of frequencies of f1 and f2. The resulting wave has a frequency of
fb= |f2 - f1| ( note absolute value in the equation)
Now we can solve the problem.

a)
Since in the first case
fb =5.5 Hz we have
=> 5.5 = |336 - f1|    ...............................   (1)
In the second case
=> 7.5 = |336 - df - f1| .......................... (2)

where df is the change in frequency due to the putty. More weight less is the frequency (negative sign is used).
From the equation 1
f1= 336 - 5.5 = 330.5 Hz then
7.5 = |336 - df - 330.5|
The new frequency is
336 - df = 7.5 + 330.5
336 - df = 338

-df = 336 - 338 = - 2 Hz

df = 2 Hz
_________
b)
It was computed earlier as
f1= 330.5 Hz

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