All I need is the formula for this. Can't remember it or what it's called, then I can solve it, thank you!

The second harmonic of a guitar string has a frequency of 120 Hz. What is the length of the guitar string if the speed of the waves on the string is 110 m/s?

To find the length of the guitar string, we can use the formula for the speed of the waves on a string:

Speed of waves on a string = frequency * wavelength

In this case, the frequency of the second harmonic is given as 120 Hz. The wavelength (λ) for the second harmonic is twice the length of the string (l), since it corresponds to a half wavelength.

So, we can rewrite the formula as:

Speed of waves on a string = frequency * (2 * length of the string)

Substituting the given values:

110 m/s = 120 Hz * (2 * length of the string)

To solve for the length of the string, divide both sides of the equation by 240 Hz:

110 m/s / 240 Hz = (2 * length of the string)

0.4583 m = 2 * length of the string

Finally, divide both sides by 2 to isolate the length of the string:

0.4583 m / 2 = length of the string

The length of the guitar string is approximately 0.22915 meters.

To find the length of the guitar string, we can use the formula for the speed of waves on a string:

v = f * λ

Where:
v = speed of waves on the string (110 m/s)
f = frequency of the wave (120 Hz)
λ = wavelength of the wave (unknown)

Since the second harmonic of a guitar string is double the frequency of the fundamental harmonic, the frequency of the fundamental harmonic can be calculated by dividing the given frequency by 2:

f₁ = 120 Hz / 2 = 60 Hz

Now we can use the formula for the wavelength of a wave on a string:

λ = (2 * L) / n

Where:
L = length of the string (unknown)
n = harmonic number (2 for the second harmonic)

Rearranging the formula, we have:

L = (n * λ) / 2

Plugging in the values, we get:

L = (2 * 110 m/s) / (60 Hz / 2)
L = (2 * 110 m/s) / 30 Hz

Simplifying the expression, we find:

L = (220 m/s) / 30 Hz

L = 7.333...

Therefore, the length of the guitar string is approximately 7.33 meters.