The third harmonic of a guitar string has a frequency of 170 Hz. What is the length of the guitar string if the speed of the waves on the string is 125 m/s?
Choose one answer.
a. 1.103 m
b. 2.206 m
c. 0.368 m
d. 2.040 m
noob
To find the length of the guitar string, we can use the formula for the fundamental frequency of a stretched string:
f = v / (2L)
where f is the frequency, v is the speed of the waves, and L is the length of the string.
In this case, we are given the third harmonic frequency (f = 170 Hz) and the speed of the waves (v = 125 m/s). We need to find the length of the string (L).
Since the third harmonic frequency is three times the fundamental frequency, we can write:
3f = v / (2L)
Rearranging the equation, we get:
L = v / (2 * 3f)
Now we can substitute the given values into the equation:
L = 125 m/s / (2 * 3 * 170 Hz)
Calculating this expression, we find:
L ≈ 0.368 m
Therefore, the correct answer is c. 0.368 m.