Question

A traveling wave in a string is given by y=0.03 sin(2.2x-3.5t) where y and x are in metres and t is in seconds. Find the amplitude, wavelength, the frequency, the period and the of the wave?

Answer 1

The traveling wave is described with the following equation:

$$y = A\sin(kx-\omega t)$$

where $A$ is the amplitude, $\omega$ is the angular frequency, and $k = 2\pi/\lambda$ is the wave number, where $\lambda$ is the wavelength. Comparing this general form with the given expression

$$y = 0.03\sin(2.2x-3.5t)$$

obtain:

$$A = 0.03m\\ \lambda = 2\pi/k = 2\pi/2.2 \approx 2.86m\\ f = \dfrac{\omega}{2\pi} = \dfrac{3.5}{2\pi} \approx 0.57Hz\\ T = 1/f \approx 1.8s$$

Answer. Amplitude 0.03m, wavelength 2.86m, frequency 0.57Hz, period 1.8s.