Not sure where to begin with this question--any help appreciated!
Two kids sitting on opposite sides of a small lake use sticks to beat the surface of the
water at a frequency f=1.5 Hz. They notice that a standing wave pattern develops between
the points where they are disturbing the water surface. They count n=5 nodes over the
L=10 m distance between them.
What can be said about the speed of wave propagation on the water surface based on
this information.
To determine the speed of wave propagation on the water surface, we can use the formula:
v = f * λ
where:
v = speed of wave propagation
f = frequency of the wave
λ = wavelength of the wave
In this problem, we are given the frequency f=1.5 Hz and the distance between the kids L=10 m.
To find the wavelength, we need to understand what a node is. In a standing wave pattern, a node is a point of zero amplitude or displacement. When the kids create a standing wave between them, the nodes represent the points where the water surface is undisturbed.
In this case, the problem states that there are n=5 nodes over the L=10 m distance between the kids. This means that there are 5 complete cycles or wavelengths between the kids.
To find the wavelength, we can divide the distance between the kids (L) by the number of cycles (n):
λ = L / n
= 10 m / 5
= 2 m
Now that we have the frequency (f = 1.5 Hz) and the wavelength (λ = 2 m), we can calculate the speed of wave propagation using the formula:
v = f * λ
= 1.5 Hz * 2 m
= 3 m/s
Based on this information, we can say that the speed of wave propagation on the water surface is 3 m/s.