Answer to Question #308117 in Mechanics | Relativity for Lipika

Question

A sound wave of frequency 300Hz travels with speed 340 m/s along the negative x-direction . Each point of the medium moves up and down through a total distance of 5.0 mm. Determine the necessary parameters to represent the wave mathematically.

Answer 1

Explanations and Calculations.

$\qquad\qquad \begin{aligned} \small \lambda&=\small \frac{v}{f}=\frac{340}{300}=1.13\,m\\ \small k&=\small \frac{2\pi}{\lambda}=\frac{30\pi}{17}=5.54\,m^{-1}\\ \small \omega&=\small 2\pi f= 600\pi=1885\, rads^{-1}\\ \\ \small y(x,t)&=\small A\sin(kx+\omega t)\\ &=\small \frac{5}{2}\sin(5.54x+1885t)\\ &=\small 2.5\sin(5.54x+1885t) \end{aligned}$