3aWave Properties and Types
Explore transverse and longitudinal waves, master the wave speed equation v = fλ, and distinguish mechanical from electromagnetic waves.
Wave properties govern everything from the pitch of a musical note to the color of light — mastering these fundamentals unlocks optics, acoustics, and modern communications technology.
How do waves transfer energy without transferring matter — and what properties define every wave?
Lesson Overview
Waves are disturbances that transfer energy through a medium or through space without permanently displacing matter. This lesson covers the two main types of waves (transverse and longitudinal), the key properties that describe every wave (wavelength, frequency, amplitude, period, and speed), and the distinction between mechanical and electromagnetic waves.
Key Concepts
Transverse Wave
Particles oscillate perpendicular to the direction of wave travel (e.g., light, water surface)
Longitudinal Wave
Particles oscillate parallel to the direction of wave travel (e.g., sound)
Wavelength (λ)
Distance between two successive identical points on a wave; unit: metres
Frequency (f)
Number of complete oscillations per second; unit: Hz (1/s)
Period (T = 1/f)
Time for one complete oscillation; unit: seconds
Wave Speed (v = fλ)
Speed at which the wave pattern travels through the medium
Worked Examples
A wave has a frequency of 440 Hz and a wavelength of 0.773 m. Calculate its speed.
A water wave has a period of 0.25 s and travels at 3.0 m/s. Find its wavelength.
Classify each wave as transverse or longitudinal: (a) light wave, (b) sound wave, (c) wave on a guitar string.
A radio station broadcasts at 98.0 MHz. The speed of electromagnetic waves is 3.00 × 10⁸ m/s. Find the wavelength.
A wave completes 60 oscillations in 3.0 seconds. Find (a) the frequency and (b) the period.
Guided Problems
External Supplemental Resource
Guided Practice Video: Wave Properties and Types
Review amplitude, period, frequency, and wavelength — and how they relate through the wave speed equation v = fλ — before completing the guided practice problems below.
Video by Khan Academy on YouTube
Watch on YouTube ↗A wave has wavelength 2.0 m and travels at 10 m/s. Find its frequency and period.
Hint: Use f = v/λ, then T = 1/f.
Explain why sound cannot travel through outer space but light can.
Hint: Think about whether each wave requires a medium to propagate.
A transverse wave on a rope has amplitude 0.05 m and wavelength 0.40 m. Sketch the wave and label the amplitude and wavelength.
Hint: Amplitude is the maximum displacement from equilibrium; wavelength is the distance between two identical adjacent points.
A microwave oven operates at 2.45 GHz. Calculate the wavelength of the microwaves. (c = 3.00 × 10⁸ m/s)
Hint: Convert GHz to Hz first: 1 GHz = 10⁹ Hz. Then use λ = v/f.
If the frequency of a wave doubles while the wave speed stays constant, what happens to the wavelength?
Hint: Use v = fλ and hold v constant.
Key Vocabulary
Wavelength (λ)
The distance between two successive identical points on a wave (e.g., crest to crest); measured in metres.
Example: Visible light has wavelengths between about 400 nm (violet) and 700 nm (red).
Frequency (f)
The number of complete wave cycles passing a point per second; unit: hertz (Hz = 1/s).
Example: Middle C on a piano has a frequency of 261.6 Hz.
Amplitude (A)
The maximum displacement of a particle from its equilibrium position; related to the energy carried by the wave.
Example: A louder sound wave has greater amplitude than a quieter one at the same frequency.
Wave Speed (v)
The speed at which the wave pattern (phase) travels through the medium; v = fλ.
Example: Sound travels at about 340 m/s in air; light travels at 3.00 × 10⁸ m/s in a vacuum.
Interactive Practice — 5 Questions
Which equation correctly relates wave speed, frequency, and wavelength?
In a longitudinal wave, particles oscillate:
A wave has period T = 0.02 s. What is its frequency?
Which of the following is an electromagnetic wave?
If wave speed doubles and frequency stays the same, the wavelength:
Independent Practice
A sound wave travels at 340 m/s and has a frequency of 850 Hz. Calculate its wavelength and period.
Explain the difference between transverse and longitudinal waves. Give two real-world examples of each.
A wave on a string has wavelength 0.60 m and period 0.030 s. Find the wave speed and frequency.
Visible light has wavelengths from 400 nm to 700 nm. Calculate the frequency range of visible light. (c = 3.00 × 10⁸ m/s)
★ Explain why the speed of a wave depends on the medium it travels through, not on the frequency or amplitude. Use the example of sound in air vs. sound in water to support your answer.
ChallengeCommon Mistakes
Thinking that a higher amplitude means a higher frequency.
Amplitude and frequency are independent properties. Amplitude relates to energy/loudness; frequency relates to pitch/color.
Confusing period and frequency — "a longer period means higher frequency."
Period and frequency are reciprocals: T = 1/f. A longer period means lower frequency.
Assuming wave speed always equals 3 × 10⁸ m/s.
Only electromagnetic waves in a vacuum travel at c. Sound, water waves, and EM waves in media all travel at different speeds.
Math Tips
Always check units: frequency in Hz, wavelength in m, speed in m/s. Then v = fλ gives m/s = Hz × m = (1/s) × m ✓
Convert prefixes before calculating: 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz, 1 nm = 10⁻⁹ m.