Question

A sinusoidal wave is described by
y (x, t) = 2.0 sin (2.11x − 3.62t) cm
where x is the position along the wave propagation. Determine the amplitude, wave
number, wavelength, frequency and velocity of the wave.

Answer 1

A sinusoidal wave is described by

$$y (x, t) = 2.0 \sin (2.11x - 3.62t) \, \text{cm}$$

where $x$ is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave.

Solution

the amplitude $A = 2.0 \, \text{cm}$

wave number $k = 2.11 \frac{1}{\text{cm}}$

wavelength $\lambda = \frac{2\pi}{k} = 2 * \frac{\pi}{2.11} = 2,99 \, \text{cm}$

frequency $f = \frac{\omega}{2\pi} = \frac{3.62}{2\pi} = 0.58 \, \text{Hz}$

velocity of the wave $v = \frac{\omega}{k} = \frac{3.62}{2.11} = 1,71 \, \frac{\text{cm}}{\text{s}}$