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?

a) 261.50 Hz and 258.50 Hz
b) 261.00 Hz and 258.00 Hz
c) 262.50 Hz and 257.50 Hz
d) 260.50 Hz and 259.50 Hz

Answer 1

The other string of the piano could have frequencies of either 261.50 Hz or 258.50 Hz, as they both would create a beat frequency of 1.50 Hz when combined with a string tuned to 260.00 Hz.

Step-by-step explanation:

In the scenario where the middle-C hammer of a piano hits two strings and produces a beat frequency of 1.50 Hz with one string tuned to 260.00 Hz, the frequencies of the other string could be either higher or lower than 260.00 Hz by the amount of the beat frequency. Therefore, the other string could have frequencies of either:

• 260.00 Hz + 1.50 Hz = 261.50 Hz
• 260.00 Hz - 1.50 Hz = 258.50 Hz

These two frequencies result in the production of beats at the rate of 1.50 Hz when combined with a string tuned to 260.00 Hz, as per the principle of superposition and interference in waves.