Question

The middle-C hammer of a piano hits two strings, producing beats of 1.60 Hz. One of the strings is turned to 260.00 Hz. What frequencies (in Hz) could the other string have?

Answer 1

The frequencies the other string could have are 258.4 Hz and 261.6 Hz.

Step-by-step explanation:

Given;

beat frequency, Fb = 1.60 Hz

frequency of the first string, F₁ = 260.00 Hz

frequency of the second string, F₂ = ?

Beat frequency is given as;

Fb = F₂ - F₁ or Fb = F₁ - F₂

Fb + F₁ = F₂ or F₂ = F₁ - Fb

1.6 + 260 = F₂ or F₂ = 260 - 1.6

261.6 Hz = F₂ or F₂ = 258.4 Hz

Therefore, the frequencies the other string could have are 258.4 Hz and 261.6 Hz.