The Electromagnetic Spectrum: Question 3

Worked solution

Part (a): The wave speed equation

For any wave, the speed, frequency and wavelength are linked by:

$v = f\lambda$

where $v$ is the wave speed in $\text{m/s}$, $f$ is the frequency in $\text{Hz}$, and $\lambda$ is the wavelength in $\text{m}$.

Part (b): Calculating the wavelength

The question tells us the signal travels at $v = 3.0\times10^{8}\text{ m/s}$.

First convert the frequency from megahertz to hertz:

$f = 2400\text{ MHz} = 2400\times10^{6}\text{ Hz} = 2.4\times10^{9}\text{ Hz}$

Rearrange $v = f\lambda$ to make wavelength the subject:

$\lambda = \frac{v}{f}$

Substitute the values:

$\lambda = \frac{3.0\times10^{8}}{2.4\times10^{9}}$

$\lambda = 0.125\text{ m}$

Rounding to 2 significant figures:

$\lambda = \boxed{0.13\text{ m}}$

Part (c): Identifying the region

A wavelength of about $0.13\text{ m}$ (roughly $13\text{ cm}$) is far shorter than typical radio-broadcast wavelengths (tens to hundreds of metres) but much longer than infrared or visible light. This places the signal in the microwave region of the electromagnetic spectrum, consistent with wireless routers, which use microwaves to send wireless internet signals.

Final answers

• (a) $v = f\lambda$
• (b) Wavelength $=$ $0.13\text{ m}$
• (c) Region $=$ microwaves