Question

The equation of a wave travelling on a string is y=0.1sin$[1.4x+314t]$.Then

In which direction does the wave travel?

Find the wave speed , the wavelength and the frequency of the wave.

What is the maximum displacement and the maximum speed of a portion of the string ?

Answer 1

Given that,

$y=\left(0.10mm\right)\sin \left[\right(31.4m^{-1})x+(314s^{-1}\left)t\right]$

(1) The wave is travelling in negative x direction.

(2) Frequency

$\omega =2\pi \nu$

$\frac{314}{2\times 3.14}=\nu$

$\nu =50Hz$

Wavelength

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

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

$\lambda =\frac{2\times 3.14}{31.4}$

$\lambda =0.2m$

Wave speed,

$v=\nu \lambda$

$v=50\times 0.2$

$v=10m/s$

(3) Maximum displacement, $a=0.10mm$