Question

A sinusoidal wave is described by 𝑦 = (0.48 𝑚) sin(0.555𝑥 − 36.0𝑡) 𝑚, where x and y are in meters

and t is in seconds. Determine for this wave the (a) amplitude, (b) angular frequency, (c) angular wave

number, (d) wavelength, (e) wave speed, and (f) direction of motion.

Answer 1

(a) $A=0.48\ m.$

(b) $\omega=36\ \dfrac{rad}{s}.$

(c) $k=0.555\ m^{-1}.$

(d)

$$k=\dfrac{2\pi}{\lambda},$$ $$\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi}{0.555\ m^{-1}}=11.32\ m.$$

(e)

$$\omega=2\pi f,$$ $$f=\dfrac{\omega}{2\pi}=\dfrac{36\ \dfrac{rad}{s}}{2\pi}=5.73\ Hz,$$ $$v=f\lambda=5.73\ Hz\times11.32\ m=64.8\ \dfrac{m}{s}.$$

(f) The wave moving in negative $x$-direction.