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Waves: Amplitude, Frequency and Wavelength
Waves & Optics
A wave is a travelling disturbance that carries energy without carrying matter. From ripples on a pond to radio signals, waves are described by the same few quantities.
What a wave is
A wave is an oscillation that travels through a medium or through space, transferring energy from one place to another. In a transverse wave the particles vibrate at right angles to the direction of travel, as in a rope shaken up and down or in a light wave. In a longitudinal wave the particles vibrate back and forth along the direction of travel, as in a sound wave, where air is alternately compressed and stretched. A wave can be drawn as a graph of displacement against distance or against time, and the same shape repeats over and over. The key quantities are amplitude, wavelength, period and frequency.
Amplitude, frequency and wavelength
Amplitude is the maximum displacement from the rest position, and it measures the energy carried by the wave: a bigger amplitude means more energy. Wavelength is the distance between two successive identical points, such as two crests, and period is the time for one complete oscillation. Frequency is the number of oscillations per second, measured in hertz, and it is the reciprocal of the period. Wave speed is frequency times wavelength, so knowing any two of speed, frequency and wavelength lets you find the third. For a wave on a string, speed depends on tension and mass per unit length, not on frequency.
Where you see it
Ocean waves carry energy to the shore, sound waves carry speech and music, and light waves carry images to your eyes. Earthquakes send seismic waves through the ground, and a stadium crowd sends a Mexican wave around the stands. In each case the disturbance moves while the material stays roughly where it was. Engineers use waves deliberately: ultrasound scans the body, sonar maps the seabed, and radio waves carry broadcasts. Understanding amplitude, frequency and wavelength is the foundation for everything that follows about sound, light and quantum physics.
Worked example: speed and period of a wave
A wave has frequency f = 5.0 Hz and wavelength lambda = 2.0 m. Use wave speed v = f lambda. Substitute: v = 5.0 x 2.0 = 10 m/s. The period is T = 1/f = 1/5.0 = 0.20 s. So the wave travels at 10 m/s and each point repeats its motion every 0.20 s. If the frequency doubled to 10 Hz at the same speed, the wavelength would halve to 1.0 m.
Common mistakes
- Confusing amplitude with wavelength: amplitude is the height of the wave from its centre line; wavelength is the distance between two identical points.
- Thinking frequency and wavelength are independent: for a given wave speed, increasing the frequency shortens the wavelength.
- Saying the particles move with the wave: in a water wave the water moves mostly up and down, while the wave pattern moves forward.
Practice questions
- A wave has frequency 2.0 Hz and wavelength 0.50 m. What is its speed?
Show answer
v = 2.0 x 0.50 = 1.0 m/s.
- What is the period of a 440 Hz sound wave?
Show answer
T = 1/440 = 0.00227 s, about 2.3 ms.
- If frequency doubles at constant wave speed, what happens to wavelength?
Show answer
The wavelength halves, because v = f lambda with v fixed.
Frequently asked questions
Does a wave carry matter along with it?
No. A wave transfers energy and information, but the particles of the medium only oscillate about fixed positions; there is no net flow of matter.
Can the speed of a wave change?
Yes, by changing the medium or its tension and temperature; for example sound travels faster in warm air than in cold air.