For the wave shown in figure, write the equation of this wave, if its position is shown at t = 0. Speed of…
For the wave shown in figure, write the equation of this wave, if its position is shown at t = 0. Speed of wave is $v = 300 \text{ ms}^{-1}$.
Solution
Sol. From figure, $\frac{5}{2}\lambda = 0.2\,\mathrm{m}$
$\therefore \lambda = 0.08\,\mathrm{m}$
$\Rightarrow f = \frac{v}{\lambda} = \frac{300}{0.08} = 3750\,\mathrm{Hz}$
Also, $k = \frac{2\pi}{\lambda} = 78.5\,\mathrm{m}^{-1}$
and $\omega = 2\pi f = 23562\,\mathrm{rad\,s}^{-1}$
At $t = 0,\; x = 0,\; \frac{dy}{dx} = \text{positive}$
and the given curve is a sine curve.
Hence, equation of wave travelling in positive x-direction should have the form,
$y(x,t) = A\sin(kx - \omega t)$
Substituting all the values in above equation, we get
$y(x,t) = 0.06\sin(78.5 x - 23562 t)\,\mathrm{m}$
Answer: $y(x,t)=0.06\sin(78.5 x - 23562 t)\,\mathrm{m}$