Question

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?

Answer 1

The possible frequencies of the other string are 258.50 Hz and 261.50 Hz.

Step-by-step explanation:

The frequency of the beat produced when two strings are played together is equal to the difference between their frequencies. In this case, the beat frequency is 1.50 Hz.

The frequency of one of the strings is given as 260.00 Hz. To find the possible frequencies of the other string, we can subtract and add the beat frequency to the frequency of the known string. Therefore, the possible frequencies of the other string are 258.50 Hz and 261.50 Hz.

If you have any further questions, feel free to ask!

Answer 2

f₂ = 261.5Hz or 258.5Hz

Step-by-step 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