Question

A wave has angular frequency 30 rad/s and wavelength 2.0 m.

What are its (a) wave number and (b) wave speed?

Short answer

The wavenumber of the wave is 3.14 rad/m.

The wave speed is 9.55 m/s.

Step-by-step solution

Given information:

The angular frequency of the wave =$\omega$= 30 rad/s

The wavelength of the wave =$\lambda$= 2.0 m.

Calculating the wavenumber:

The formula to calculate the wavenumber is given by $k=\frac{2\pi }{\lambda }$

Substitute 2m for $\lambda$to calculate the wavenumber:

$$\begin{gathered} k=\frac{2\times 3.14}{2m} \\ =3.14rad/m \end{gathered}$$

Therefore, the wavenumber is 3.14 rad/m.

Calculating the wave speed:

The formula to calculate the frequency of the wave is $f=\frac{\omega }{2\pi }$

Substitute 30 rad/s for $\omega$to calculate the frequency of the wave.

$$\begin{gathered} f=\frac{30rad/s}{2\pi } \\ =4.77Hz \end{gathered}$$

The formula to calculate the wave speed( assuming to be a periodic wave) is given by

$v=\lambda f$

Substitute 2m for $\lambda$and 4.77 Hz for f into the above formula to calculate the wave speed.

$$\begin{gathered} v=2m\times 4.77Hz \\ =9.55m/s \end{gathered}$$

Therefore, the wave speed is 9.55 m/s.