Question

The equation of a progressive wave travelling along a string is given by $y=0.00425sin(2.52t-52x)$ where the numerical constant are in SI units. Find the amplitude, wave number, propagation constant, period and speed of the wave.

Answer 1

Given that,

$y=0.00425\sin (2.52t-52x)........\left(1\right)$

The equation of progressive wave is given by

$y=a\sin (\omega t-kx).............\left(2\right)$

On comparing these two equations

Amplitude of wave $A=0.00425m$

Wave number

$K=\frac{2\pi }{\lambda }$

$\lambda =\frac{6.28}{52}=0.12m$

$wavenumber\overline{\lambda }=\frac{1}{\lambda }=\frac{1}{0.12}=8.33$

Propagation constant $K=52m^{-1}$

Frequency

$\omega =2\pi \nu$

$\upsilon =\frac{\omega }{2\pi }=\frac{2.52}{6.28}=0.4012Hz$

Time period $T=\frac{1}{\nu }=\frac{1}{0.4012}=2.49s$

Speed of wave

$v=\nu \lambda$

$=0.4012\times 0.12$

$=0.048m/s$