Posted by
**susan** on
.

Two sinusoidal waves travel in the same direction and have the same frequency. Their amplitudes are Y1 and Y2. The smallest possible amplitude of the resultant wave is:

a) Y1 + Y2 and occurs if they are 180 degrees out of phase

b)[Y1 - Y2] and occurs if the are 180 degrees out of phase

c) Y1 + Y2 and occurs if they are in phase

d) [y1-Y2] and occurs if they are in phase

e) [Y1-Y2] and occurs if they are 90 out of phase

My thoughts:

All the explainations of resultants in my book for waves show Y1+Y2=Resultant for the theory of superposition. So I think then to get the smallest wave it would be A. Y1 + Y2 if they are 180 degrees out of phase.

The displacement of a string is given by

y(x,t)=Ysin(Kx + wt)

speed of the wave is

a)2pik/w

b)w/K

c)wk

d)2pi/k

e)k/2pi

Work:

v=lamba*f

k=2pi/lambda

w=2pi/T

v=2pi/lambda * 2pi/(1/f)

v=w/k

so I choose b

Help is appreciated :)