The wave function y(x,t)for a standing wave on a string fixed at both ends is given by y(x,t)= 0.080 sin 6.0x cos 600t where the units are SI.The wavelength of this wave is
A)6.00 m
B)1.05 m
C)600 m
D)0.010 m
E)impossible to tell given this information about the standing wave.

Question

Quizplus · Accepted Answer

In a standing wave fixed at both ends, the boundary conditions require that the ends of the wave must be nodes. Therefore, the wavelength of the standing wave is twice the distance between the ends, or:
λ = 2L
where L is the length of the string.
In this problem, we are not given the length of the string, but we can use the fact that the standing wave has six nodes (points of zero displacement) between the two ends. The distance between adjacent nodes is λ/2, so the length of the string is:
L = (3/2)λ
We can now solve for the wavelength:
λ = 2L/3 = 2/3(3/2) = 1.0 m
Therefore, the best choice is B) 1.05 m.

The Wave Function Y(x,t)for a Standing Wave on a String