You want to set up a standing wave on a string that has a length of 3.7 m. You find that the lowest frequency that will work is 46 Hz. What is the speed of a wave on this string?
To determine the speed of a wave on a string, we can use the formula:
speed = frequency * wavelength
In this case, we are given the frequency as 46 Hz. To find the wavelength, we need to consider the nature of standing waves on a string.
For a standing wave on a string, the length of the string can be divided into segments called "nodal points" or "nodes." These nodes occur at intervals where the string does not appear to be moving. The distance between two consecutive nodes is equal to half of a wavelength (λ/2).
In this problem, we have the length of the string as 3.7 m, and the lowest frequency that will work is 46 Hz. The lowest frequency corresponds to the fundamental mode, where the string has one node at each end.
So, we can determine the wavelength as follows:
wavelength = 2 * length of string = 2 * 3.7 m = 7.4 m
Now, we can substitute the values into the formula to find the speed:
speed = frequency * wavelength = 46 Hz * 7.4 m = 338.4 m/s
Therefore, the speed of the wave on the string is 338.4 m/s.