The middle-C hammer of a piano hits two strings, producing beats of 1.60 Hz. One of the strings is turned to 250.00 Hz. What frequencies (in Hz) could the other string have? (Answer to the nearest 0.1 Hz.)

248.5Hz or 251.5Hz

Explanation:

Given :

Beat frequency, Fbeat = 1.5 Hz

Frequency of string 1, f1 = 250 Hz

Frequency of string 2, f2 =?

Recall:

Fbeat = |f1 - f2|

1.5 = 250 - f2

f2 = 250 - 1.5

f2 = 248.5 Hz

OR

- Fbeat = |f1 - f2|

- 1.5 = 250 - f2

f2 = 250 + 1.5

f2 = 251.5 Hz

Hence, the two possible frequencies of the other string are 248.5Hz or 251.5Hz