A 1.0 m length of string has fixed attachments at both ends. The wave speed on the string is 400 m/s and the frequency is 800 Hz. What is the fundamental frequency of the string?
To determine the fundamental frequency of the string, we need to use the formula:
Frequency = Wave speed / wavelength
We are given the wave speed (400 m/s), but we need to find the wavelength. Let's calculate it.
Wavelength is defined as the distance between two consecutive points in a wave that are in phase. For the fundamental frequency, this would be the distance between the two fixed attachments of the string.
Given that the length of the string is 1.0 m, the wavelength can be calculated as twice the length of the string.
Wavelength = 2 * length
Wavelength = 2 * 1.0 m
Wavelength = 2.0 m
Now we can substitute the values into the frequency formula to find the fundamental frequency:
Frequency = Wave speed / wavelength
Frequency = 400 m/s / 2.0 m
Frequency = 200 Hz
Therefore, the fundamental frequency of the string is 200 Hz.