What is the fundamental frequency for a 60 cm banjo string if the speed of waves on the string is 480 m/s?
To find the fundamental frequency of a banjo string, we need to use the formula:
f = (v / λ)
where:
f is the frequency,
v is the speed of the wave, and
λ is the wavelength.
In this case, the speed of the wave on the string is given as 480 m/s, and we need to find the fundamental frequency for a 60 cm banjo string.
To determine the wavelength, we need to consider that the fundamental frequency produces a standing wave with one full wave cycle, which means the wavelength is twice the length of the string.
Converting the length of the string to meters, we have:
λ = 2 * (60 cm) = 1.2 m
Now, we can use the equation to calculate the fundamental frequency:
f = (480 m/s) / (1.2 m) = 400 Hz
Therefore, the fundamental frequency for a 60 cm banjo string with a wave speed of 480 m/s is 400 Hz.
recall that v = λf
f = v/λ = 480m/s ÷ .6m = 800/s = 800 Hz