The speed of waves in a particular guitar string is 390 m s‒1. Determine thefundamental frequency (1st harmonic) of the string if its length is 35.5 cm

Sure, here's how to calculate the fundamental frequency (1st harmonic) of the string:

Step 1: Convert the length of the string from cm to m. This is because the speed of the wave is given in m/s. So, 35.5 cm = 0.355 m.

Step 2: The formula for the speed of a wave is v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. For a string, the wavelength of the fundamental frequency (1st harmonic) is twice the length of the string. So, λ = 2 * 0.355 m = 0.71 m.

Step 3: Rearrange the formula to solve for the frequency: f = v / λ.

Step 4: Substitute the given values into the formula: f = 390 m/s / 0.71 m = 549.3 Hz.

So, the fundamental frequency of the string is approximately 549.3 Hz.