Answer to Question #90872 in Physics for pritika

Question

A 265 Hz sound wave travels with a speed of
330 ms-1along the x-axis. Each point of the
medium moves up and down through
6.0 mm. Write down the expression for the
wave. Calculate the (i) wavelength of the
wave, and (ii) velocity and acceleration of the
particles of the medium.

Answer 1

The expression for the wave

$$y=A \sin{(2\pi(ft-x\lambda))}$$

$$y=0.0060\sin{(2\pi(265t-1.25x))}$$

i)

$$\lambda=\frac{c}{f}=\frac{330}{265}=1.25 \ m$$

ii) The velocity of the particles of the medium:

$$v=2\pi(265)0.0060\cos{(2\pi(265t-1.25x))}$$

$$v=10\cos{(2\pi(265t-1.25x))}$$

The acceleration of the particles of the medium:

$$a=-(2\pi(265))^2 0.0060\sin{(2\pi(265t-1.25x))}$$

$$a=-17000\sin{(2\pi(265t-1.25x))}$$