What is the fundamental frequency for a 62 cm banjo string if the speed of waves on the string is 470 m/s?
The fundamental wavelength is 0.124 m (twice the string length), and the frequency is the wave speed divided by that number.
470/0.124 = 3790 Hz
That seems high to me. Almost 4 octaves above middle C
To find the fundamental frequency of a vibrating string, we can use the equation:
f = v / λ
where:
f is the frequency,
v is the speed of waves on the string, and
λ is the wavelength of the wave.
Given:
v = 470 m/s (speed of waves on the banjo string)
To find the wavelength, we need to know the length of the string. In this case, the length of the banjo string is given as 62 cm.
Since wavelength is defined as the distance between two consecutive peaks (or troughs) of a wave, we can convert the length of the string to meters:
λ = length of the string / 100
So, λ = 62 cm / 100 = 0.62 m
Now, we can substitute the values into the equation:
f = v / λ
f = 470 m/s / 0.62 m
Simplifying the expression:
f = 758.06 Hz
So, the fundamental frequency of the 62 cm banjo string is approximately 758.06 Hz.