Answer to Question #184127 in Mechanics | Relativity for Akinola

Question

The particle displacement y of air molecules due to a sound wave is given by

y=0.008coswtsinkz where k=4π÷m and w=50πrads/s.

Calculate:

I) the distance between 2 consecutive nodes

ii) the amplitude after 0.565s

Answer 1

i) the distance between 2 consecutive nodes is

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

ii) the amplitude after 0.565s is

$$A_y=0.008\cos(50\pi·0.565)=1.75·10^{-4}\text{ m}.$$