Answer to Question #184970 in Civil and Environmental Engineering for John Prats

Question

A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x,t)=2.00 cos(15.7x-858t), where is micrometers, x is in meters, and t is in seconds. Calculate the amplitude, wavelength and the speed of the wave.

Answer 1

when provided with an equation

 s(x,t)=2.00 cos(15.7x-858t),

 s(x, t) = A cos (k x + ω t)

A= amplitude

so amplitude = $2.0 \times 10^{-6} \mu m$

if k= 15.7 then wavelength $\lambda = \frac{2\pi}{k} = \frac{2\pi}{15.7}$

$\lambda= 0.4002 m$

Speed of wave $\nu= \frac{\omega}{k} = \frac{-858}{15.7}$

$\nu=$ 54.6497 m/s in opposite direction