Question

You need to use your cell phone, which broadcasts an 830 MHz signal, but you’re in an alley between two massive, radio- wave-absorbing buildings that have only a 15 m space between them. What is the angular width, in degrees, of the electromagnetic wave after it emerges from between the buildings?

Answer 1

Answer:Angular width of the electromagnetic wave after it emerges from between the buildings is 2.761 degree

Explanation:

The wavelength of the electromagnetic wave is

$\lambda=\frac{c}{f} \\\lambda=\frac{3\times 10^8}{830\times 10^6} \\\lambda=0.361 m$

Consider two buildings as a single slit, for single slit diffraction dark fringes are located an angle of

$\theta _{p}=sin^{-1}\frac{\lambda}{a}$

where $\lambda$ is frequency, $a$ is space between buildings.

For the first dark fringes

$\theta _{1}=sin^{-1}\frac{\lambda}{a}\\\theta _{1}=sin^{-1}\frac{0.3614}{15}\\\theta _{1}=1.38^{0}$

Angular width of the electromagnetic wave after it emerges from between the buildings is

$\Delta\theta =2\theta _{1}\\\Delta\theta =2\times 1.38\\\Delta\theta =2.761^0$