Question

A piano tuner hears a beat every 2.00 s when listening to a 264.0-Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

a) (266.0 Hz) and (262.0 Hz)
b) (267.0 Hz) and (263.0 Hz)
c) (268.0 Hz) and (262.0 Hz)
d) (269.0 Hz) and (261.0 Hz)

Answer 1

The two possible frequencies of the piano string are 262.0 Hz and 266.0 Hz.

Step-by-step explanation:

To determine the possible frequencies of the piano string, we need to understand how beats are produced. Beats occur when two sounds of slightly different frequencies interfere with each other. The beat frequency is equal to the difference between the frequencies of the two sounds.

In this case, the beat frequency is 2.00 Hz. Since the tuning fork has a frequency of 264.0 Hz, we can set up an equation to find the possible frequencies of the piano string: 264.0 Hz - f = 2.00 Hz, where f is the frequency of the piano string.

Solving for f gives us f = 262.0 Hz. Therefore, the two possible frequencies of the piano string are 262.0 Hz and 266.0 Hz (option a).