Waves of all wavelengths travel at the same speed v on a given string. Traveling wave velocity and wavelength are related by v=lambda*f,where v is the wave speed, lambda is the wavelength (in meters), and f is the frequency [in hertz]. Since only certain wavelengths fit properly to form standing waves on a specific string, only certain frequencies will be represented in that string's standing wave series. The frequency of the nth pattern/harmonic is f_n = v/lambda_n = v/(2L/n) = n*v/{2L}. Note that the frequency of the fundamental is f_1 = v / (2L), so f_n can also be thought of as an integer multiple of f_1: f_n = n*f_1. Now, the question. Assume the frequency of the fundamental of the guitar string is 320 Hz. At what speed v do waves move along that string? Use the guitar's length from previous question.

To find the speed at which the waves move along the guitar string, we need to use the equation v = lambda * f, where v is the wave speed, lambda is the wavelength, and f is the frequency.

We are given that the frequency of the fundamental (f_1) of the guitar string is 320 Hz. The equation for the frequency of the nth harmonic is f_n = n * f_1.

We are also given that the guitar's length, denoted by L, was determined in a previous question.

Since we need to find the speed v, we are looking for the relationship between v, lambda, and f.

The equation for the frequency of the nth pattern/harmonic can be written as f_n = v / lambda_n, where lambda_n is the wavelength of the nth harmonic.

Using the formula for the wavelength of the nth harmonic (lambda_n = 2L / n), we can substitute for lambda_n in the equation for f_n:

f_n = v / (2L / n)

Simplifying further, we have:

f_n = (n * v) / (2L)

Now we can substitute the frequency of the fundamental f_1 into the equation:

f_1 = v / (2L)

Therefore, we can write f_n as an integer multiple of f_1:

f_n = n * f_1

By comparing this equation with the previous one, we can see that:

(n * v) / (2L) = n * f_1

Simplifying further, we obtain:

v = 2L * f_1

Given that the frequency of the fundamental (f_1) is 320 Hz, and the length of the guitar string (L) was determined in the previous question, it is now possible to calculate the speed v using the above equation.