Question

The equation of certain traveling waves: y(x,t)=0.0450 sin(25.12x-37.68t-0.523) where x
and y are in meters, and t in seconds. Determine the following: (a) Amplitude, (b) wave number, (c)
wavelength, (d) angular frequency, (e) frequency, (f) phase angle, (g) the wave propagation speed.

Answer 1

$y(x,t)=0.0450 \sin(25.12x-37.68t-0.523)$

Comparing this with standard equation $y(x,t)=A\sin(kx-\omega t+\phi)$

Amplitude(A)=0.045 m

$k=2\pi/\lambda\\\lambda=2\pi/k$

$\lambda=2\pi/25.12=0.25$

Wavelength = 0.25

wave number = 1/ wavelength =$1/0.25=4$

angular frequency $=\omega=37.68$

$w=2\pi v\\v= \omega/2\pi=6$

Frequency=6 Hz

Phase angle=$\phi$=-0.523

Wave propagation speed=$\omega/k=37.68/25.12=1.5m/s$