A typical steel B-string in a guitar resonates at its fundamental frequency at 240 Hertz. The length of the string is 0.620 m. What is the wave velocity along the string? Find your answer in m/s.
What is the formula to solve?
Try this one, which you should memorize:
(frequency)*(wavelength) = wave speed
The trick is to know that, for the fundamental frequency, the wavelength is twice the length of the string, because only a half-wave is vibrating.
29.75m/s?
To find the wave velocity along the string, you can use the formula:
velocity (v) = frequency (f) x wavelength (λ)
However, in this case, we are given the frequency (240 Hz) and we need to find the wavelength. The formula to calculate wavelength is:
wavelength (λ) = length (L) / number of nodes (n)
Since a B-string in a guitar typically has one node at each end, the number of nodes (n) is 2. Therefore, the formula becomes:
wavelength (λ) = length (L) / 2
Now, substituting the given values into the formula:
wavelength (λ) = 0.620 m / 2 = 0.310 m
Finally, we can calculate the wave velocity (v) by multiplying the frequency (f) and the wavelength (λ):
velocity (v) = frequency (f) x wavelength (λ) = 240 Hz x 0.310 m = 74.4 m/s
Therefore, the wave velocity along the string is 74.4 m/s.