Question

While attempting to tune the note c at 523 hz, a piano tuner hears 2 beat/s between a reference oscillator and the string. a. what are the possible frequencies of the string? b. when the piano tuner tightens the string slightly, she hears 3 beat/s. what is the frequency of the string now?

Answer 1

The possible frequencies for the piano string when 2 beats per second are heard compared to a 523 Hz oscillator are 521 Hz and 525 Hz. After tightening the string, with 3 beats per second, the piano string's frequency is 526 Hz.

Step-by-step explanation:

When a piano tuner hears 2 beats per second between a reference oscillator at 523 Hz and a piano string, the possible frequencies of the string could be either 523 Hz + 2 Hz = 525 Hz or 523 Hz - 2 Hz = 521 Hz. These are the two possible frequencies because beats occur due to the interference of two sound waves of slightly different frequencies, and the rate of the beats is equal to the absolute difference between those frequencies.

After the tuner tightens the string, the frequency of the string increases and the beats are heard at 3 beats per second. Since tightening the string would increase the frequency, the new frequency of the string would be 523 Hz + 3 Hz = 526 Hz.