Question

consider the wave function y(x,t)=(3.00 cm)sin(0.4 m-1x+2.00s-1t + pie/10). what are the period, wavelength, speed, and initial phase shift of the wave modeled by the wave function?

Answer 1

Given:

$$y(x,t)=3.00\sin(0.4x+2.00t + \pi/10)$$

The general form of wave equation is given by

$$y(x,t)=A\sin\left(\frac{2\pi}{\lambda}x+\frac{2\pi}{T}t + \phi_0\right)$$

Hence we get:

a) The period

$$T=2\pi/2.00=\pi=3.14\:\rm s$$

b) The wavelength

$$\lambda=2\pi/0.4=15.7\:\rm m$$

c) The speed of wave

$$v=\lambda/T=15.7/3.14=5\:\rm m/s$$

d) The initial phase shift

$$\phi_0=\pi/10$$