A typical steel B-string in a guitar resonates at its fundamental frequency at 240 Hertz. The length of the string is 0.640 m. What is the wave velocity along the string?
307.2
To find the wave velocity along the string, we can use the formula:
v = f * λ
where v is the velocity, f is the frequency, and λ is the wavelength.
First, we need to find the wavelength (λ). In this case, since we know the length of the string (L) is 0.640 m, and the fundamental frequency (f) is 240 Hz, we can calculate the wavelength using the formula:
λ = 2L/n
where n is the harmonic number. For the fundamental frequency, n = 1.
λ = 2 * 0.640 m / 1
λ = 1.280 m
Now, we can substitute the frequency and wavelength values into the formula to find the wave velocity (v):
v = 240 Hz * 1.280 m
v = 307.2 m/s
Therefore, the wave velocity along the steel B-string is 307.2 m/s.