The middle-C hammer of a piano hits two strings, producing beats of 1.50 Hz. One of the strings is tuned to 260.00 Hz. What frequencies could the other string have?

f₂ = 261.5Hz or 258.5Hz

Explanation:

The beat frequency = / f₁ - f₂/

where f₁ and f₂ are the frequencies of individua waves

f (beat) = 1.5Hz

f₁ (frequency of one string) = 260Hz

f (beat) = / f₁ - f₂/

1.5Hz = / 260Hz - f₂/

to solve this equation

we make it into two seprate equation and solve it separately

260Hz - f₂ = 1.5Hz

f₂ = 260Hz - 1.5Hz

= 258.5Hz

260Hz - f₂ = - 1.5Hz

f₂ = 260Hz + 1.5Hz

= 261.5Hz

therefore, the two possible frequencies of the other strings are

f₂ = 258.5Hz or 261.5Hz