Question

. The equation of a sinusoidal wave is y=0.4 sin 10π (3t+2x) where x and y are in
metre and t is in second. Find the amplitude, wavelength, frequency and velocity of wave

Answer 1

Given equation is,

$\quad$

$\sf{y=0.4\sin[10\pi(3t+2x)]}$

$\quad$

We change the equation as follows.

$\quad$

$\sf{y=0.4\sin(20\pi x+30\pi t)}$

$\quad$

When compared to this one, the standard equation for such sinusoidal wave should be,

$\quad$

$\sf{y=A\sin(kx+\omega t)}$

$\quad$

Then compared, we get,

$\quad$

$\sf{\underline {\underline {A=0.4\ m}}}\\\\\\\\\sf{k=\dfrac {2\pi}{\lambda}=20\pi}\\\\\\\implies\ \underline {\underline {\sf{\lambda=0.1\ m}}}\\\\\\\\\sf{\omega=2\pi\nu=30\pi}\\\\\\\implies\ \sf{\underline {\underline {\nu=15\ Hz}}}\\\\\\\\\sf{\underline {\underline {v=\nu\lambda=1.5\ ms^{-1}}}}$

Answer 2

Explanation:

plz check the image

answer is 1.5ms