Answer to Question #288772 in Physics for NICKO

Question

Transverse waves on a string have a wave speed 8.00 m/s, amplitude 0.0700 m, and

wavelength 0.320 m. The waves travel in the -x-direction, and at t = 0, x = 0, the end of

the string has its maximum upward displacement. (a) Find the frequency, period, and

wave number of these waves. (b) Write a wave function describing the wave. (c) Find

the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s

Answer 1

Given:

$v=8.00\:\rm m/s$

$A=\rm 0.0700\: m$

$\lambda=0.320\: \rm m$

(a) the frequency

$$f=\frac{v}{\lambda}=\frac{8.00}{0.320}=25.0\:\rm Hz$$

the period

$$T=\frac{1}{f}=\frac{1}{25.0}=0.0400\:\rm s$$

the wave number

$$k=\frac{2\pi}{\lambda}=\frac{6.28}{0.320}=19.6\:\rm m^{-1}$$

(b) the wave function describing the wave

$$y(x,t)=A\cos(2\pi ft-kx)\\ y(x,t)=0.0700\cos (157t-19.6x)$$

(c)

$$y=0.0700\cos (157*0.150-19.6*0.360)\\ =-0.0495\:\rm m$$