A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?
A)240 Hz
B)246 Hz
C)254 Hz
D)259 Hz
E)263 Hz

Question

Quizplus · Accepted Answer

The difference between the frequencies of the tuning forks is 255 Hz - 250 Hz = 5 Hz. Since the string produces 4 beats per second with the 250 Hz tuning fork and 9 beats per second with the 255 Hz tuning fork, the frequency of the string must be somewhere in between these two values.

One way to find the frequency of the string is to take the average of these two values, which is (250 Hz + 255 Hz)/2 = 252.5 Hz. However, another approach is to find the frequency that produces a difference of 5 beats per second, which would correspond to half of a wavelength of the string.

Thus, the frequency of the string can be calculated as follows:

frequency of string = average of tuning fork frequencies ± (beats per second/2)
frequency of string = 252.5 Hz ± (5 beats/s)/2
frequency of string = 252.5 Hz ± 2.5 Hz
frequency of string = 250 Hz or 255 Hz

Since the beats are more frequent with the 255 Hz tuning fork, it is likely that the frequency of the string is closer to 255 Hz than 250 Hz. Therefore, the best choice is B) 246 Hz.

A Guitar String Produces 4 Beats/s When Sounded with a 250