An infrared wave has a wavelength of 1.5 × 10−6 m in air. What is its frequency? (speed of electromagnetic waves = 3.0 × 108 m/s)
- v = fλ, so f = v ÷ λ.
- f = (3.0 × 108) ÷ (1.5 × 10−6).
- 3.0 ÷ 1.5 = 2.0, and 108 ÷ 10−6 = 1014.
Answer: 2.0 × 1014 Hz
Electromagnetic spectrum
O Level / IGCSE Physics · Waves. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
The idea
Light is one member of a family of waves called the electromagnetic spectrum. All of them are transverse waves, all can travel through a vacuum, and in a vacuum all travel at the same speed, 3.0 × 108 m/s. The speed in air is almost the same.
The members differ in frequency and wavelength. Radio waves have the lowest frequency and the longest wavelength. Gamma rays have the highest frequency and the shortest wavelength.
Waves with a higher frequency carry more energy and are more dangerous. Ultraviolet, X-rays and gamma rays are ionising: they can damage cells and cause cancer. Microwaves and infrared mainly cause heating.
Rules to remember
- Order of increasing frequency (decreasing wavelength): radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
- Speed of all electromagnetic waves in a vacuum = 3.0 × 108 m/s; use v = fλ.
- Radio waves: radio and television broadcasts, astronomy. Microwaves: satellite television, mobile phones, Bluetooth, microwave ovens.
- Infrared: remote controllers, thermal imaging, intruder alarms, optical fibres, electric grills.
- Ultraviolet: security marking, detecting fake bank notes, sterilising water. It can cause skin cancer and cataracts.
- X-rays: medical scanning and security scanners. Gamma rays: sterilising food and medical equipment, detecting and treating cancer.
- Too much microwave or infrared radiation heats body tissue and causes burns.
Common mistake
Students think gamma rays or X-rays travel faster than radio waves because they carry more energy. In a vacuum every electromagnetic wave has the same speed; only the frequency and wavelength differ.
Worked example
Practice questions
Try each one, then open the answer.
1. Which electromagnetic wave has the longest wavelength?
- Agamma rays
- Bultraviolet
- Cradio waves
- DX-rays
Show answer
Answer: C. Radio waves have the longest wavelength and lowest frequency. Gamma rays have the shortest wavelength.
2. A radar pulse is sent towards an aircraft, and its reflection returns 2.0 × 10−4 s later. How far away is the aircraft? (speed of radio waves = 3.0 × 108 m/s)
- A0.033 m
- B3.0 km
- C30 km
- D60 km
Show answer
Answer: C. The pulse goes there and back: total distance = 3.0 × 108 × 2.0 × 10−4 = 6.0 × 104 m. The aircraft is half of this away, 3.0 × 104 m = 30 km. Forgetting to halve gives 60 km; 0.033 m uses the speed of sound.
3. Why are X-rays, and not visible light, used to make an image of a broken bone?
- AX-rays are reflected by skin but pass through bone
- BX-rays pass through soft tissue but are absorbed by bone
- CX-rays travel faster than light, so the image is sharper
- DX-rays are not ionising, so they are completely safe
Show answer
Answer: B. Visible light cannot pass through skin. X-rays pass easily through flesh but are absorbed strongly by dense bone, so the bone casts a shadow on the detector. X-rays are ionising, so doses are kept small.