A wave on a string has a period of 0.20 s and a wavelength of 0.60 m. What is the wave speed?
- Find the frequency: f = 1 ÷ T = 1 ÷ 0.20 = 5.0 Hz.
- Use the wave equation: v = fλ = 5.0 × 0.60.
- v = 3.0 m/s.
Answer: 3.0 m/s
Transverse and longitudinal waves and wave properties
Physics · Waves. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A wave carries energy from one place to another. The matter it travels through only oscillates about a fixed position; it does not travel along with the wave.
In a transverse wave the oscillations are at right angles to the direction of energy transfer. Ripples on water and all electromagnetic waves are transverse. In a longitudinal wave the oscillations are parallel to the direction of energy transfer, making compressions and rarefactions. Sound in air is longitudinal.
Four quantities describe a wave: amplitude, wavelength, frequency and period. The wave equation links speed, frequency and wavelength, and it works for every kind of wave.
Rules to remember
- Amplitude: the maximum displacement of a point on the wave from its undisturbed position, in m.
- Wavelength (λ): the distance from a point on one wave to the equivalent point on the next wave, in m.
- Frequency (f): the number of waves passing a point each second, in Hz.
- period = 1 ÷ frequency (T = 1/f), with T in s and f in Hz.
- wave speed = frequency × wavelength (v = fλ), in m/s.
- Ripple tank: frequency = number of waves ÷ time; wavelength = distance across several waves ÷ number of waves.
- Speed of sound in air: speed = distance ÷ time, using a large distance so the time is long enough to measure.
Common mistake
Students measure amplitude from crest to trough. That distance is twice the amplitude: amplitude is measured from the undisturbed position to a crest.
Worked example
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