Electromagnetic Waves Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electromagnetic Waves.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Transverse waves consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation.

Light, radio, X-rays—all are EM waves, just different frequencies.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electromagnetic Waves asks what oscillates, what travels, and which wave quantity is being measured.

Common stuck point: Students often know a formula related to electromagnetic waves but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?

Worked Examples

Example 1

easy
An electromagnetic wave has a frequency of 6×1014 Hz6 \times 10^{14} \text{ Hz}. What is its wavelength? What type of EM radiation is this? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Answer

λ=500 nm (visible light, blue-green)\lambda = 500 \text{ nm (visible light, blue-green)}

First step

1
All EM waves travel at the speed of light: λ=cf\lambda = \frac{c}{f}.

Full solution

  1. 2
    λ=3×1086×1014=5×10−7 m=500 nm\lambda = \frac{3 \times 10^8}{6 \times 10^{14}} = 5 \times 10^{-7} \text{ m} = 500 \text{ nm}
  2. 3
    This is in the visible light range, corresponding to blue-green light.
Electromagnetic waves are oscillating electric and magnetic fields that travel at the speed of light. They do not require a medium and can travel through a vacuum.

Example 2

medium
How long does it take light from the Sun to reach Earth? The Sun-Earth distance is 1.5×1011 m1.5 \times 10^{11} \text{ m} and c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A microwave oven operates at a frequency of 2.45×109 Hz2.45 \times 10^9 \text{ Hz}. What is the wavelength of the microwaves? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Example 2

hard
A WiFi router transmits at 5 GHz5 \text{ GHz} with a power of 0.1 W0.1 \text{ W}. What is the wavelength? If the signal spreads uniformly in all directions, what is the intensity at 10 m10 \text{ m}? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Example 3

easy
In what medium can electromagnetic waves travel that sound waves cannot?

Example 4

easy
What is the speed of an electromagnetic wave in vacuum?

Example 5

easy
In an EM wave, the electric field and magnetic field are oriented how relative to each other?

Example 6

easy
A radio wave has frequency f=1×108 Hzf = 1 \times 10^8 \text{ Hz}. Find its wavelength in vacuum.

Example 7

easy
Are electromagnetic waves transverse or longitudinal?

Example 8

easy
Light travels from the Sun to Earth across mostly empty space. What does this tell you about light?

Example 9

easy
A green light wave has wavelength λ=5×10−7 m\lambda = 5 \times 10^{-7} \text{ m}. Find its frequency.

Example 10

easy
Do all electromagnetic waves carry energy?

Example 11

medium
An EM wave in vacuum has period T=2×10−15 sT = 2 \times 10^{-15} \text{ s}. Find its wavelength.

Example 12

medium
A radio station broadcasts at λ=300 m\lambda = 300 \text{ m}. What is its frequency in MHz?

Example 13

medium
An EM wave enters glass and slows to 2×108 m/s2 \times 10^8 \text{ m/s}. Its frequency stays 5×1014 Hz5 \times 10^{14} \text{ Hz}. Find the wavelength in glass.

Example 14

medium
A laser pulse travels 9×108 m9 \times 10^8 \text{ m} through vacuum. How long does it take?

Example 15

medium
A microwave has frequency f=3×109 Hzf = 3 \times 10^9 \text{ Hz}. Find its wavelength in vacuum (in cm).

Example 16

medium
Two EM waves in vacuum: wave A at f=6×1014f = 6\times10^{14} Hz, wave B at f=3×1014f = 3\times10^{14} Hz. Which travels faster?

Example 17

medium
An X-ray has wavelength λ=1×10−10 m\lambda = 1 \times 10^{-10} \text{ m}. Find its frequency in vacuum.

Example 18

medium
Sunlight takes about 500 s500 \text{ s} to reach Earth in vacuum. Estimate the Earth-Sun distance.

Example 19

medium
An EM wave has frequency f=2×1014f = 2 \times 10^{14} Hz. What is its period?

Example 20

challenge
An EM wave has wavelength 600 nm600 \text{ nm} in vacuum. It enters a medium where its speed is 34c\tfrac{3}{4}c. Find its wavelength in the medium.

Example 21

challenge
A pulsed EM source emits at f=1×109f = 1\times10^9 Hz. In one period, how far does the wave front advance in vacuum?

Example 22

challenge
Radar sends an EM pulse to an object and the echo returns 4×10−74\times10^{-7} s later. How far away is the object?

Example 23

easy
In vacuum, what is cc in m/s?

Example 24

easy
An EM wave has frequency 5×109 Hz5\times10^9\,\text{Hz}. Find its wavelength in vacuum.

Example 25

easy
An EM wave has λ=0.5 m\lambda = 0.5\,\text{m}. Find its frequency.

Example 26

easy
Light travels 9×109 m9\times10^9\,\text{m} in vacuum. How long does that take?

Example 27

medium
An EM wave has period T=1×10−8 sT = 1\times10^{-8}\,\text{s}. Find its wavelength.

Example 28

medium
In a glass of refractive index n=1.5n = 1.5, an EM wave originally at λ=600 nm\lambda = 600\,\text{nm} enters. Find the wavelength in glass (frequency stays the same).

Example 29

medium
A pulse echoes off a wall in 4 μs4\,\mu\text{s} in air (cc accurate). How far is the wall?

Example 30

medium
An EM wave has f=1.5×1014 Hzf = 1.5\times10^{14}\,\text{Hz}. Find its wavelength in vacuum and identify the region.

Example 31

medium
A radar beam travels to a plane 30 km30\,\text{km} away and reflects back. Find the round-trip time.

Example 32

medium
An EM wave's electric field amplitude is E0=600 V/mE_0 = 600\,\text{V/m}. Find the magnetic field amplitude B0B_0.

Example 33

medium
How long does light take to travel 1 km1\,\text{km} in vacuum?

Example 34

medium
An AM radio station broadcasts at λ=600 m\lambda = 600\,\text{m}. Find its frequency in kHz.

Example 35

medium
An EM wave in water (refractive index n=1.33n = 1.33) has vacuum wavelength 500 nm500\,\text{nm}. Find its speed and wavelength in water.

Example 36

hard
A plane EM wave has amplitude E0=300 V/mE_0 = 300\,\text{V/m}. Find the intensity (use I=12ϵ0cE02I = \tfrac{1}{2}\epsilon_0 c E_0^2, ϵ0=8.85×10−12 F/m\epsilon_0 = 8.85\times10^{-12}\,\text{F/m}).

Example 37

hard
A 50 W50\,\text{W} isotropic light source. Find the intensity at r=5 mr = 5\,\text{m}.

Example 38

hard
An EM wave has B0=5×10−7 TB_0 = 5\times10^{-7}\,\text{T}. Find the corresponding E0E_0.

Example 39

hard
An EM wave travels through a material at v=1.5×108 m/sv = 1.5\times10^8\,\text{m/s}. Find the refractive index nn.

Example 40

challenge
A laser beam in vacuum has intensity I=1000 W/m2I = 1000\,\text{W/m}^2. Find the peak electric field E0E_0 (use I=12ϵ0cE02I = \tfrac{1}{2}\epsilon_0 c E_0^2, ϵ0c≈2.654×10−3 S/m\epsilon_0 c \approx 2.654\times10^{-3}\,\text{S/m}).
← Back to Electromagnetic Waves Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

wavestransverse wave