Answer to Question #159649 in Physics for Hilario Encarnacion

Question

The wave function that describes a certain transverse wave at initial time t=0 is

y(x,t)=(7.20mm)sin2π(x/0.3m - t/0.0400s)

Find the wave's

a) amplitude

b) wavelength

c) frequency

d) speed of propagation

e) period

f) wave number

g) direction of propagation

Answer 1

The wave function that describes a certain transverse wave 

$$y(x,t)=y_{\rm max}\sin\left(\frac{2\pi}{\lambda}x-\frac{2\pi}{T}t\right)$$

In our case

$$y(x,t)=(7.20 \:{\rm mm}) \sin\left(\frac{2\pi}{0.3\:\rm m}x-\frac{2\pi}{0.04\:\rm s}t\right)$$

a) amplitude

$$y_{\rm max}=7.20 \:{\rm mm}$$

b) wavelength

$$\lambda=0.3\:\rm m$$

c) frequency

$$f=\frac{1}{T}=\frac{1}{0.04\:\rm s}=25\:\rm Hz$$

d) speed of propagation

$$v=f\lambda=25*0.3=7.5\:\rm m/s$$

e) period

$$T=0.04\:\rm s$$

f) wave number

$$k=\frac{2\pi}{0.3\:\rm m}=21\:\rm m^{-1}$$

g) direction of propagation of the wave is negative $x$ direction.