A wave travels along a rope at 6.0 m/s. The distance between neighbouring crests is 1.5 m. What is the frequency of the wave?
- Crest to crest is one wavelength, so λ = 1.5 m.
- v = fλ, so f = v ÷ λ.
- f = 6.0 ÷ 1.5 = 4.0 Hz.
Answer: 4.0 Hz
General properties of waves
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
A wave carries energy from one place to another without carrying matter. The particles of the material only vibrate about their rest positions; they do not travel along with the wave.
In a transverse wave the vibrations are at right angles to the direction the energy travels, as in water waves and light. In a longitudinal wave the vibrations are parallel to that direction, as in sound.
All waves can be reflected, refracted and diffracted. Refraction is a change of direction caused by a change of speed. Diffraction is the spreading of a wave after it passes through a gap or round an edge.
Rules to remember
- wave speed = frequency × wavelength (v = fλ), with v in m/s, f in Hz and λ in m.
- Frequency: the number of waves passing a point each second. Time for one wave (period) = 1 ÷ frequency.
- Wavelength: the distance between two neighbouring identical points, such as crest to crest.
- Amplitude: the maximum distance from the rest position (not from crest to trough).
- Transverse: electromagnetic waves, water surface waves, seismic S-waves. Longitudinal: sound, seismic P-waves.
- Water waves going from deep to shallow water slow down. The wavelength gets shorter and the frequency stays the same.
- Diffraction through a gap is greatest when the gap is about the same size as the wavelength. Longer wavelengths spread more round an edge.
Common mistake
Students measure the amplitude from the top of a crest to the bottom of a trough. That distance is twice the amplitude, so halve it.
Worked example
Practice questions
Try each one, then open the answer.
1. What is the frequency of a wave?
- Athe distance between two successive crests
- Bthe number of wavelengths passing a point per second
- Cthe maximum displacement from the rest position
- Dthe time for one complete wave
Show answer
Answer: B. Frequency is the number of complete waves (wavelengths) passing a point per unit time, measured in hertz. The time for one wave is the period.
2. On a wave, the vertical distance from the top of a crest to the bottom of a trough is 8.0 cm. What is the amplitude of the wave?
- A2.0 cm
- B4.0 cm
- C8.0 cm
- D16 cm
Show answer
Answer: B. Amplitude is measured from the rest (middle) position to a crest, which is half the crest-to-trough distance: 8.0 ÷ 2 = 4.0 cm.
3. Water waves of wavelength 3.0 cm travel at 12 cm/s in deep water. They pass into shallow water, where their speed is 8.0 cm/s. What is their wavelength in the shallow water?
- A1.5 cm
- B2.0 cm
- C3.0 cm
- D4.5 cm
Show answer
Answer: B. The frequency is set by the source and does not change: f = 12 ÷ 3.0 = 4.0 Hz. In shallow water λ = v ÷ f = 8.0 ÷ 4.0 = 2.0 cm. Multiplying by 12/8 instead of 8/12 gives 4.5 cm.
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