Question

Two transverse sinusoidal waves combining in a medium are described by the wave functions y1 = 3.00 sin π(x - 0.600t), y2 = 3.00 sin π(x - 0.600t) where x, y1, and y2 are in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at (a) x=0.250 cm, (b) x =0.500 cm, and (c) x = 1.50 cm. (d) Find the three smallest values of x corresponding to antinodes.

Answer 1

Answer:

Explanation:

The interfering waves have form y

1

​

=Asin(kx−ωt) and y

2

​

=Asin(kx+ωt)

Thus the resultant wave has displacement y=y

1

​

+y

2

​

=2Asin(kx)cos(ωt)

Maximum displacement is obtained when cos(ωt)=1

Thus y

max

​

=2×3×sin(π×0.25)=4.24cm