Waves and the wave speed equation
A wave carries energy from one place to another without carrying the material along with it. One equation links how fast it travels to how often it wobbles and how long each wave is.
Part 1 of 3: Learn it
In short
- Transverse waves oscillate at right angles to the direction of travel; longitudinal waves oscillate along it.
- Wave speed = frequency × wavelength, v = f λ.
- Period T = 1 ÷ f: a wave of 50 Hz has a period of 0.02 s.
Where this is in your specification
Spec points: AQA 4.6.1.1 and 4.6.1.2, Edexcel Topic 4, OCR P5.1 (J249) and P4.1 (J250)
| Board | Topic: Waves and the electromagnetic spectrum |
|---|---|
| AQA 8463 | 4.6.1.1, 4.6.1.2 and 4.6.2 (8463); 6.6 (8464) |
| Edexcel 1PH0 | Topics 4 and 5 |
| OCR J249 | P5 (J249), P4.1 and P4.2 (J250) |
Two kinds of wave
| Transverse | Longitudinal | |
|---|---|---|
| Oscillation | at right angles to the direction the energy travels | parallel to the direction the energy travels |
| Examples | ripples on water, light and all electromagnetic waves | sound, and the P-waves from earthquakes |
| Features | peaks (crests) and troughs | compressions and rarefactions |
In both, the wave moves the energy along while each bit of the medium only oscillates about where it started. A floating cork bobs up and down as ripples pass under it.
Describing a wave
- Amplitude: the maximum displacement from the rest position (measure from the middle line to a peak, not peak to trough).
- Wavelength (λ): the distance from one point on a wave to the same point on the next, such as peak to peak, in metres.
- Frequency (f): the number of waves passing a point each second, in hertz (Hz).
- Period (T): the time for one complete wave, in seconds. T = 1 ÷ f.
The wave speed equation
Speed in m/s, frequency in Hz, wavelength in m. You can also find wave speed as distance ÷ time, for example by timing an echo (remember the sound travels there and back).
The required practical
In a ripple tank, a stroboscope or a photo freezes the waves so you can measure the length of ten waves and divide by ten for λ, and count waves passing a point in 10 s for f. On a stretched string driven by a vibration generator, measure the length of several half-wavelengths at a known frequency. In both, v = f λ gives the speed.
A sound wave has a frequency of 680 Hz and a wavelength of 0.50 m. What is its speed?
Show the answer
v = 680 × 0.50 = 340 m/s.
Part 2 of 3: See it worked
Worked examples
Example 1
Water waves in a ripple tank have a frequency of 5.0 Hz and a wavelength of 4.0 cm. What is their speed?
- λ = 4.0 cm = 0.040 m
- v = f λ = 5.0 × 0.040
- v = 0.20 m/s
Answer: 0.20 m/s.
Example 2
A radio wave travels at 3.0 × 10⁸ m/s with a frequency of 100 MHz. Find its wavelength.
- f = 100 MHz = 1.0 × 10⁸ Hz
- λ = v ÷ f = 3.0 × 10⁸ ÷ 1.0 × 10⁸
- λ = 3.0 m
Answer: 3.0 m.
Common mistakes
- Measuring amplitude from peak to trough. That is twice the amplitude.
- Leaving wavelength in cm or frequency in kHz.
- Saying the water travels with the wave. Only the energy does.
- Forgetting to halve the distance in an echo question.
What is the period of a wave with a frequency of 20 Hz?
Show the answer
T = 1 ÷ 20 = 0.05 s.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
A sound wave has a frequency of 680 Hz and a wavelength of 0.50 m. What is its speed?
v = 680 × 0.50 = 340 m/s.
What is the period of a wave with a frequency of 20 Hz?
T = 1 ÷ 20 = 0.05 s.
Is sound transverse or longitudinal?
Longitudinal: the air particles oscillate along the direction the sound travels.
Jobs that use this
- Studio sound engineer (opens a new tab)
- Network engineer (opens a new tab)
- Meteorologist (opens a new tab)
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses