Question

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The frequency of the piano's:____________.

A) 444 Hz
B) 880 Hz
C) 436 Hz
D) either 436 Hz or 444 Hz

Answer 1

D) either 436 Hz or 444 Hz

Step-by-step explanation:

frequency of the tuning fork, F₁ = 440 Hz

frequency of the piano, F₂ = ?

Beat frequency, F = 4 Hz

Beat frequency is given as the difference between the frequency of the two instruments and it is given by;

F = F₂ - F₁ or F = F₁ - F₂

F₂ = F + F₁ or F - F₁ = - F₂

F₂ = 4 Hz + 440 Hz or 4 - 440 = - F₂

F₂ = 444 Hz or - 436 = - F₂

F₂ = 444 Hz or F₂ = 436 Hz

Therefore, the frequency of the piano is 444 Hz or 436 Hz