Question

(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics:
A = 8.00 cm, l = 80.0 cm, f = 3.00 Hz, and y(0, t) = 0 at t = 0.
(b) What If?
Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at the point x = 10.0 cm.

Answer 1

Answer: (a) y(x,t) = 0.0800 sin(7.85x + 6πt) meters

Remember y(0, 0) must equal 0.

(b) 0 = sin (.785 + φ)

Explanation: (a)

k = 2π/λ

k = 2π/0.800

k = 7.85 m-1

ω = 2πf

ω = 2π3

ω = 6π rad/sec.

y(x,t) = 0.0800 sin(7.85x + 6πt) meters

Remember y(0, 0) must equal 0.

(b)

We know that we must shift the wave so that y(0.100, 0) = 0

y(x,t) = 0.0800 sin(7.85x + 6πt + φ)

0 = 0.08 sin (7.85(0.1) + 0 + φ)

0 = sin (0.785 + φ)

φ = -0.785