3. A transverse wave on a string has an amplitude A. A tiny spot on the string is colored red. As one cycle of the wave passes by, what is the total distance traveled by the red spot? (a) A (b) 2A (c) A (d) 4A (e) A

2. Consider a very long string held taut by two students, one on each end. Student A oscillates the end of the string producing a wave modeled with the wave function Y₁(x,t) = a sin (kx-oot) and student B oscillates the string producing at twice the frequency, moving in the opposite direction. Both waves move at the same speed v =. The two waves interfere to form a resulting wave whose wave function is Y(x,t) = Y₁(x,t) + Y₂(x,t). Find the velocity of the resulting wave using the linear wave equation d²Y(x,t) 1 d²Y(x,t) dx² v² dt²

1. A progressive wave travelling along the positive x-direction is represented by y(x, t) = A sin (kx - oot + o). Its snapshot at t = 0 is given in the figure. ↑ A ↓ M For this wave, the phase o is π (a) (b) π 2 (c) 0 (d) E|N 2

4. A travelling wave on a string is given by: = 5.7(cos(3.3x) cos(4.4t) – sin(3.3x) sin(4.4t)) y = For this wave find (a) its velocity of propagation (b) the transverse velocity (c) the transverse acceleration (d) the maximum displacement, velocity and acceleration of a particle on the string.

1. Two transverse waves travel through a taut string. The speed of each wave if v= 21.00 m/s. A plot of the vertical position as a function of the horizontal position is shown below for the time t=0.00s. y(m) A Y1(x, t) Y2(x, t) 4 3 1 x(m) -1 -2 -3 -4 + 4 6. 10 12 14 16 18 20 a) What is the wave length of each wave? m 12 = b) What is the frequency of each wave? f = Hz f2 = Hz c) What is the maximum vertical speed of the oscillating particles of each string? V1 max- m/s V2max m/s