Two piano strings are supposed to be vibrating at 220 Hz , but a piano tuner hears three beats every 3.2 s when they are played together. f one is vibrating at 220 Hz , what must be the frequency of the other (is there only one answer)

Explanation:

The frequency beat is give n by the expression:

fb = | f1 -f2 |      ( 1 )

that is, the absolute value of the difference between the frequencies of the waves. But also the fb is the radio between beats and time:

fb = beats/time = 3/3.2 = 0.93 Hz

By replacing in the formula ( 1 ) :

f2 = 220 Hz + 0.93 Hz = 220.93 Hz

f2 = 220 Hz - 0.93 Hz = 219.07 Hz

But we take the value 220.93 Hz ≈ 221 HZ because a piano can support this frequency.

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