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Chapter 19: Problem 37

A tuning fork of unknown frequency makes three beats per second with a standard fork of frequency \(384 \mathrm{~Hz}\). The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork?

Short Answer

Expert verified
The frequency of the unknown tuning fork is 387 Hz.

Step by step solution

01

Understand the Beats Frequency

The beat frequency is the absolute difference between the frequencies of the two tuning forks. Therefore, we have two possible frequencies for the unknown fork: 384 Hz + 3 Hz = 387 Hz or 384 Hz - 3 Hz = 381 Hz.
02

Understanding the Effect of Wax

Putting a small piece of wax on a prong of the first fork lowers its frequency. If the beat frequency decreases when we add the wax, it means the frequency of the unknown fork originally must have been higher than 384 Hz.
03

Conclusion

Drawing on the findings above, the unknown frequency could only be 387 Hz since it must decrease when we add wax. The wax makes the tines of the fork heavier, which makes them vibrate more slowly, and thus reduces the pitch (frequency). This would bring the beat frequency closer to the known 384 Hz fork, which means the original unknown frequency must have been higher.

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