Finding the period of an oscillation...?

Question

The A string of a violin is a little too tightly stretched. Four beats per second are heard when the string is together with a tuning fork that is oscillating accurately at concert A (440 Hz).

What is the period of the violin string oscillation?

Explain your work. Thanks!

Answer 1

1/444 second. With 4 beats/sec, the violin string and the tuning fork are in phase 4 times per sec. This happens when the frequencies differ by 4 Hz. Since it's too taut, it's vibrating at a frequency above 440 Hz, thus at 444 Hz. Period = 1/frequency = 1/444 sec..

Answer 2

Concert A 440