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A guitar string under the tension of 200N, vibrating in its fundamental mode, gives 6beats/s. With...

A guitar string under the tension of 200N, vibrating in its fundamental mode, gives 6beats/s. With turning fork the player increases the string tension to 242N and a gain gets 6beats/s. find the frequency of the turning fork.

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Answer #1

When the string is in T1 = 200 N tension frequency be f1

Then

- f1 = 6

and

When the string is in T2 = 242 N tension frequency be f2

2-f=6

Add these 2 equations to obtain

12 - f1 = 12

and frequency is proportional to square root of tension

f2/f1 = T2/T= 242/200 = 1.1

or

12 = 1.181

Therefore plug this in the previous equation

1.1f1-f1 = 12

or

f1 = 12/0.1 = 120 Hz

Therefore the frequency of the tuning fork is

f = fi + 6 = 120 + 6 = 126 Hz

answer is 126 Hz

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