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
1.103 m
To find the length of the guitar string, we can use the formula:
Frequency (f) = (n * velocity) / (2 * length)
where:
- f is the frequency of the harmonic (given as 170 Hz)
- n is the harmonic number (given as 3)
- velocity is the speed of the waves on the string (given as 125 m/s)
- length is the length of the guitar string (unknown)
Rearranging the formula, we have:
Length = (n * velocity) / (2 * frequency)
Plugging in the given values:
Length = (3 * 125) / (2 * 170)
Length = 375 / 340
Length = 1.103
So, the length of the guitar string is approximately 1.103 meters. Therefore, the correct answer is option 1.103 m.