Question

A wave on a string is described by the equation y(x,t) = 4.2 cos (3000 rad/s t + 5.0 rad/m x)

where t is measured in s and x is measured in mm.

(a) What is the amplitude of this wave?

(b) What are the frequency and wavelength of the wave?

(c) What is the velocity of the wave?

Answer 1

(a) $A=4.2\ m.$

(b)

$$f=\dfrac{\omega}{2\pi}=\dfrac{3000\ \dfrac{rad}{s}}{2\pi}=477.5\ Hz.$$ $$\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi}{5.0\ \dfrac{rad}{m}}=1.26\ m.$$

(c)

$$v=f\lambda=477.5\ Hz\cdot1.26\ m=602\ \dfrac{m}{s}.$$