A piano tuner is adjusting the tension for the string that plays A above middle

Question

A piano tuner is adjusting the tension for the string that plays A above middle C on a piano. She strikes her 440 Hz tuning fork, then plays the A440 key (with the sustain pedal held down), and hears 3 beats per second. (a) At what two possible frequencies could the piano be string be vibrating? While the string and tuning fork are still vibrating, she very gradually increases the tension on the string and hears the beat frequency very gradually decrease from 3 beats per second to 2 beats per second. (b) Now she knows there is only one possible frequency at which the string can be vibrating. What is that frequency?

Explanation / Answer

A. Possible frequency that she can hear are 443Hz or 437Hz

B She will play frequency note of 441 Hz Because its tension has been increased so its fundamental freqquency has been already increased and if she notice that if there is only 2 beat means 443-2 =441.

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