Question

1. A traveling wave in a string is given by where y and x are in meters and t in seconds. Find the amplitude, wavelength, the frequency, the period and the speed of the wave.

Answer 1

A transverse wave is described by the following equation:

$$y(x,t)=A\text{ sin}⁡(kx-\omega t).$$

Amplitude: $A$

Wavelength:

$$\lambda=\frac{2\pi}{k}.$$

Frequency:

$$f=\frac{\omega}{2\pi}.$$

Period:

$$T=\frac{1}{f}=\frac{2\pi}{\omega}.$$

Speed:

$$v=\frac{\omega}{k}.$$