Question

A wave is represented by y = (3.00m) sin Ɵ (2.5t -3.14x). Find the (a) amplitude, (b) angular frequency, (c) frequency, (d) wave number, (e) wavelength, and (f) speed of the wave.

Answer 1

(a) $A=3.0\ m.$

(b) $\omega=2.5\ \dfrac{rad}{s}.$

(c)

$$\omega=2\pi f,$$ $$f=\dfrac{\omega}{2\pi}=\dfrac{2.5\ \dfrac{rad}{s}}{2\pi}=0.4\ Hz.$$

(d) $k=3.14\ m^{-1}.$

(e)

$$\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi}{3.14\ m^{-1}}=2\ m.$$

(f)

$$v=f\lambda=0.4\ Hz\times2\ m=0.8\ \dfrac{m}{s}.$$