Question

A traveling wave is described by the function y(x,t) = 2 cos(3pi*t − 4pi*x), where y is in cm, x is in meters, and t is in seconds.

a. In what direction is the wave traveling?

b. What is the speed of the wave?

c. What is the transverse acceleration of the wave at y = 0 and t = 1 second?

d. Write an expression for the second harmonic of this wave (i.e., same speed, but twice the frequency).

Answer 1

(a)

Let 37 – 411 = Constant

t = Constant + - 4710 3л

As x increases t decreases , therefore wave is travelling towards the negative x-direction.

(b)

2л № 21 v=X+ frequency = 2 * : * * 25 - 4 31 * - = 0.75 m/s

(c)

= a = (37)? * 2 * cos(37 - 47.0)

y=0 implies, cos(3nt – 472) = 0

Therefore,

a = 0 m/s2

(d)

When frequency is doubled , wavelength gets halved to maintain speed.

Therefore

W = 2w and k' = 2k

;

y = 2 * cos(6nt – 87.)