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You have two tuning forks that have a beat frequency of 2 Hz with respect to each other. One of them has a frequency of 440 Hz, but you do not know the frequency of the other. You place a small piece of clay on the other, an amount just capable of decreasing its resonance frequency by 1 Hz, and you repeat the experiment. This time the beat frequency is 3 Hz. From this information, what is the frequency of the other tuning fork (when it has no clay on it)?

A. 442 Hz
B. 440 Hz
C. 438 Hz
D. 436 Hz

User Cheyne
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1 Answer

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Final answer:

The frequency of the unknown tuning fork before clay was added is 438 Hz as this value generates a beat frequency of 2 Hz initially and after decreasing by 1 Hz, the beat frequency changes to 3 Hz, which is consistent with the problem statement.

Step-by-step explanation:

The student is asking about the frequency of a tuning fork given the beat frequency when sounded with a tuning fork of known frequency. Beat frequency arises when two sounds of slightly different frequencies interfere with each other, which is a concept from physics. Initially, the unknown tuning fork has a beat frequency of 2 Hz with a fork of 440 Hz. After adding clay and decreasing the frequency of the unknown fork by 1 Hz, the beat frequency becomes 3 Hz.

To find the frequency of the other tuning fork, we need to consider two possibilities due to the nature of beats: the unknown frequency could be higher or lower than 440 Hz. Therefore, we have either 440 Hz + beat frequency or 440 Hz - beat frequency.

In the first case, the other tuning fork could have been 440 Hz + 2 Hz = 442 Hz, but after placing the clay, the frequency would decrease to 441 Hz, thus making the new beat frequency 440 Hz - 441 Hz = -1 Hz (which is not a possibility since beat frequency is always a positive number).

In the second case, the fork could have been 440 Hz - 2 Hz = 438 Hz originally, and after placing the clay, it would become 437 Hz, which would yield a beat frequency of 440 Hz - 437 Hz = 3 Hz. This matches the situation described after placing the clay.

Therefore, the correct answer is C. 438 Hz, which was the frequency of the second tuning fork before clay was added.

User Manoj Lodhi
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