Question

 A plane wave is described by an electric field

180πcos10 (2π 100 ).

8 E  t  y

What is its (i) frequency in Hz, (ii) wave number, (iii) phase velocity, 

(iv) wavelength, and (v) direction of propagation?

Answer 1

Consider a plane wave:

$$x(y,t)=180π\text{cos}(10y+2π 100t).$$

(i) frequency in Hz:

$$f=\frac{\omega}{2\pi}=\frac{2\pi100}{2\pi}=100\text{ Hz}.$$

(ii) wave number is the term before y:

$$k=10\text{ m}^{-1}.$$

(iii) phase velocity:

$$v=\frac{\omega}{k}=\frac{2\pi 100}{10}=20\pi\text{ m/s}.$$

(iv) wavelength:

$$\lambda=\frac{2\pi}{k}=0.2\pi\text{ m}.$$

(v) direction of propagation: toward positive x.