Question

Two sinusoidal waves travelling in opposite directions interfere to produce a standing wave described by the equation
y = (1.5 m) sin (0.400x) cos (200 t)
where, x is in metres and t is in seconds. Determine the wavelength, frequency and speed of the interfering waves.

Answer 1

For a standing wave represented by $y=Asin\left(kx\right)cos\left(\omega t\right)$,

$k=\frac{2\pi }{\lambda }$ and $\omega =2\pi \nu$

where $\lambda ,\nu$ are the wavelength and frequency respectively of the interfering waves.

Thus $0.4=\frac{2\pi }{\lambda }$

$⟹\lambda =15.7m$

$200=2\pi \nu$

$⟹\nu =31.8Hz$

Speed of interfering waves is given by $\frac{\omega }{k}=500m/s$