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.
a) What can be said about the speed of wave propagation on the water surface based on
this information.
L = (n/2)lambda
lambda = 2L/5 = 2*10/5 = 4
v = lambda*f
v = 4 * 1.5 = 6 m/s
To determine the speed of wave propagation on the water surface, we can use the formula:
v = f * λ,
where v is the velocity, f is the frequency, and λ is the wavelength.
In this case, the frequency f is given as 1.5 Hz. However, we need to calculate the wavelength λ using the information given.
The distance L between the two kids is 10 m. The number of nodes n is given as 5.
In a standing wave pattern, the distance between consecutive nodes or antinodes is equal to half the wavelength. Since there are 5 nodes over a distance of 10 m, there must be 6 equally spaced points (including the ends) defining the nodes and antinodes.
The distance between these points is L/(n+1) = 10/(5+1) = 10/6 = 1.67 m.
Since the distance between consecutive nodes is half the wavelength, the wavelength can be calculated as 2 times the distance between consecutive nodes:
λ = 2 * 1.67 m = 3.34 m.
Now that we have the wavelength, we can use the formula v = f * λ to calculate the velocity:
v = 1.5 Hz * 3.34 m = 5.01 m/s.
Therefore, based on the information provided, the speed of wave propagation on the water surface is approximately 5.01 m/s.