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?
1.103 m
2.206 m
0.368 m
2.040 m
B?
To find the length of the guitar string, we can use the formula for the nth harmonic of a string:
fn = (n/2L) * v
Where:
- fn is the frequency of the harmonic
- n is the harmonic number
- L is the length of the string
- v is the speed of the waves on the string
In this case, we know that the frequency of the third harmonic (n = 3) is 170 Hz, and the speed of the waves on the string (v) is 125 m/s. We need to solve for L.
Rearranging the formula, we have:
L = (n/2fn) * v
Substituting the known values:
L = (3/2 * 170 Hz) * 125 m/s
L = (3/2 * 170 Hz) * 125 m/s
L = (3/2 * 170) * 125
L = 2.040 m
Therefore, the length of the guitar string is approximately 2.040 m. So, the correct answer is option 2.206 m.