Question

Tuning a piano to tune middle c on a piano, a tuner hits the key and at the same time sounds a 261 hz tuning fork. Part A: If the tuner hears 3 beats per second, what are the possible frequencies of the piano key? Express your answer as a whole number. If there is more than one answer, separate them by a comma.

Answer 1

The possible frequencies of the piano key when a tuner hears 3 beats per second are 258 Hz and 264 Hz.

Step-by-step explanation:

When a piano tuner hits a key on the piano and sounds a 261 Hz tuning fork, they hear 3 beats per second. In this case, the beat frequency is the difference between the frequency of the tuning fork and the frequency of the piano key. To find the possible frequencies of the piano key, we can use the formula:

Beat frequency = |f_tuning fork - f_piano key|

Substituting the given values, we have:

3 Hz = |261 Hz - f_piano key|

Solving for the frequency of the piano key, we find two possible solutions:

1. 261 Hz - 3 Hz = 258 Hz
2. 261 Hz + 3 Hz = 264 Hz

Therefore, the possible frequencies of the piano key are 258 Hz and 264 Hz.