Waves and space · GCSE Physics
Wave speed
Teacher-written GCSE Physics revision on wave speed: v = fλ with a full substitution, v = d/t, converting MHz and centimetres, and why speed is a property of the medium in ripple-tank practicals.
Wave speed v = fλ. Frequency in hertz, wavelength in metres, speed in m/s. Write the equation, convert units, substitute, then calculate.
The important bits
What you need to know
- 1
Wave speed v = fλ, where f is frequency in hertz (s⁻¹) and λ is wavelength in metres. The product is metres per second.
- 2
Wave speed is also v = d / t for a wave travelling a measured distance in a measured time. Use this in ripple tanks and echo questions.
- 3
The speed of a wave is set by the medium (and conditions such as tension or depth), not by how hard you shake the source. Shaking faster raises f and cuts λ so that v stays the same.
- 4
In a vacuum all EM waves have v = 3.0 × 10⁸ m/s. Sound in air is about 340 m/s. Water ripples are typically around 0.1–0.4 m/s in a school tank.
- 5
Convert: 1 MHz = 1 × 10⁶ Hz, 1 kHz = 1 × 10³ Hz, 1 cm = 0.01 m, 1 nm = 1 × 10⁻⁹ m. Most wrong answers are conversion errors.
- 6
Period links as v = λ / T because f = 1/T. Same substitution, different given data.
- 7
Required practical: measure f from a dipper or by timing many waves, measure λ with a ruler (several wavelengths for a mean), then v = fλ. Or time a wavefront across a known distance.
- 8
Echo: 2d = vt if the sound goes to a wall and back. Students forget the factor of two and halve the distance by accident.
Quotations worth analysing
Short evidence. Real method.
“Wave speed = frequency × wavelength”
The equation only works if f is in Hz and λ is in m. 100 MHz must become 1.00 × 10⁸ Hz before you multiply.
“The speed of a wave depends on the medium, not on the frequency you set at the source.”
Raise the dipper frequency and the ripples pack tighter. They do not race across the tank twice as fast.
Go deeper
v = fλ only works if the units match
Frequency in hertz is s⁻¹. Wavelength must be in metres, not centimetres. A radio station at 100 MHz is 1.00 × 10⁸ Hz. In air, v is 3.00 × 10⁸ m/s, so λ = v/f = 3.00 m. Students leave frequency in megahertz and get a wavelength of 3 million metres. The speed in a string depends on tension and the string, not on how fast you waggle your hand; waggling faster raises f and cuts λ so that v stays the same. That is a classic ripple-tank result. If a question gives time for a wave to travel a measured distance, use v = d/t first, then find f or λ. Write every conversion on the page: 20 cm = 0.20 m, 5.0 Hz already in SI, v = 5.0 × 0.20 = 1.0 m/s — too fast for a typical tank, so check whether λ was 2.0 cm not 20 cm.
Go deeper
Echoes and tanks are the same equation in wellingtons
A sonar pulse takes 0.040 s to return from a sea-bed. If v = 1500 m/s in seawater, the there-and-back distance is vt = 60 m, so depth d = 30 m. Forgetting the return journey doubles the depth. In a ripple tank, a strobe can freeze the pattern so you can measure several λ with a ruler and divide. Time twenty waves with a stopwatch to find f = 20 / t; one wave is too short to time accurately. Then v = fλ. The practical is not about pretty photographs; it is about reducing uncertainty with multiples. If the water is shallower, speed usually falls, and you should see λ fall at the same f. That is refraction waiting to happen at a depth boundary.
See the idea in action
A ripple tank produces waves of frequency 5.0 Hz. Ten wavelengths occupy 20 cm, so λ = 2.0 cm = 0.020 m. v = fλ = 5.0 × 0.020 = 0.10 m/s. If the frequency is raised to 10 Hz and the speed in the water stays 0.10 m/s, the new wavelength is λ = v/f = 0.10 / 10 = 0.010 m. The waves look tighter; they do not travel twice as fast. Checking with v = d/t: a wavefront crossing 0.30 m of tank in 3.0 s also gives 0.10 m/s. The two methods agree, which is the point of the practical.
Exam technique
Turn knowledge into marks
Write v = fλ, convert MHz to Hz and cm to m, substitute with units, then calculate. If frequency rises in the same medium, expect λ to fall. For echoes, use 2d = vt.
Common mistakes
Do not give these marks away
- 01
Leaving frequency in kilohertz or megahertz, or wavelength in centimetres, inside v = fλ.
- 02
Assuming that doubling frequency doubles wave speed in the same tank.
- 03
Forgetting the factor of two in echo or sonar distances.
A sound wave has frequency 200 Hz and wavelength 1.7 m. What is its speed?
A0.0085 m/s
B118 m/s
C340 m/s
D200 m/s
Show the answer
340 m/s. v = fλ = 200 × 1.7 = 340 m/s, a typical speed of sound in air. Always multiply frequency by wavelength in metres.
Quick questions
If this is the bit you searched
What is the wave-speed equation?
v = fλ. Speed in m/s equals frequency in Hz times wavelength in m. You can also use v = d/t for a measured journey.
Does changing frequency change wave speed?
Not in the same uniform medium in the usual GCSE model. Frequency up, wavelength down, product v constant. Speed changes if the medium changes.
How do you measure wave speed in a ripple tank?
Measure frequency and wavelength, then v = fλ, or time a wavefront across a known distance and use v = d/t. Measure several wavelengths to reduce uncertainty.
How do you convert 88 MHz to hertz?
Multiply by 1 × 10⁶: 88 MHz = 8.8 × 10⁷ Hz. Then λ = v/f with v = 3.0 × 10⁸ m/s in air.