Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

1.5.3Electricity, Energy and Waves

Wave Equations — WJEC GCSE Science (Double Award) - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 31 of 36

📚 WJEC GCSE Science (Double Award) - Physics Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read

Section 1 of 9The wave equation

The speed of a wave is the distance a crest travels each second. In one period T a crest travels one wavelength λ, so the speed is v = λ / T. Since f = 1 / T, this becomes the wave equation:

v = f λ

What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
The wave equation
v = wave speed in metres per second (m s−1)
f = frequency in hertz (Hz)
λ = wavelength in metres (m)

It applies to all wavessound, water, light and the rest of the electromagnetic spectrum.

Section 2 of 9Rearranging

f = v / λ and λ = v / f.

1
Use a triangle with v on top and f and λ at the bottom if it helps, but always write the working.
2
Make sure the units are consistent.
3
If the wavelength is in centimetres, convert it to metres first.
4
If the frequency is in kHz or MHz, convert it to Hz.

The speed of a wave is the distance divided by the time as for any speed, so v = d / t also applies to wave pulses, for example finding the speed of sound from an echo.

Section 3 of 9What decides the speed, frequency and wavelength

The frequency of a wave is set by the source and does not change when the wave moves into a new medium.

Medium
The speed is set by the medium.
Since v = f λ and f is fixed, the wavelength changes in proportion to the speed.
So when a wave slows down on entering a new medium, its wavelength is smaller.
This idea explains refraction (see Reflection and Refraction).

Typical speedssound in air about 340 m s−1, sound in water about 1500 m s−1, sound in steel about 5000 m s−1, and electromagnetic waves in a vacuum 3.0 × 108 m s−1.

Section 4 of 9Using the equation on graphs

For a fixed wave speed, a graph of wavelength against 1/frequency is a straight line through the origin with gradient v.

Using the equation on graphs
A graph of frequency against wavelength for a fixed speed is a curve that falls as wavelength increases (an inverse relationship): doubling the frequency halves the wavelength.
This pattern is why the electromagnetic spectrum can be drawn in a single line with long-wavelength waves having low frequency and short-wavelength waves high frequency.

Section 5 of 9Measuring wave speed in practice

In a ripple tank, you can count the waves passing a mark in a known time, or use a stroboscope to freeze the pattern, measure the wavelength over several waves for accuracy, and calculate v = f λ.

Measuring wave speed in practice
Measuring across 5 or 10 wavelengths and dividing reduces the uncertainty compared with measuring one.
The same relation is used in the experiment on the speed of sound (see Investigating the Speed of Sound).

Section 6 of 9Common exam problem types

Wave equation problems come in a few standard forms.

Common exam problem types
First, the direct calculation: given two of v, f and λ, find the third.
Second, the two-medium problem: the frequency stays the same and v and λ change together, so v1/λ1 = v2/λ2.
Third, the echo problem,
  • which combines v = d / t with the fact that the sound travels there and back,
  • so the distance to the reflector is half the total distance travelled.

An example of the third typea ship's sonar sends a pulse and receives the echo 0.60 s later.

Common exam problem types
The speed of sound in sea water is 1500 m s−1.
The total distance is 1500 × 0.60 = 900 m, so the sea bed is 450 m below the ship.
Many mistakes come from forgetting the factor of two.

Fourth, the dependence on a graph

  • if you plot v against f for a fixed wavelength, you get a straight line through the origin with gradient λ.
  • Check that you can read the gradient and give it a unit of metres.

Section 7 of 9Worked examples

  1. A ripple tank wave has frequency 8.0 Hz and wavelength 2.5 cm. Calculate its speed.

  2. A radio station broadcasts at 98 MHz. The speed of radio waves is 3.0 × 108 m s−1. Find the wavelength.

  3. A sound wave of frequency 680 Hz travels at 340 m s−1 in air and then enters water where its speed is 1500 m s−1. Find the wavelength in each.

Section 8 of 9Key terms

TermMeaning
Wave equationv = f λ; links speed, frequency, wavelength
Wave speedDistance travelled by the wave each second
HertzUnit of frequency
MediumMaterial that sets the wave speed
Inverse relationshipAs one quantity doubles, the other halves

Section 9 of 9Exam technique

1
Using the wavelength in cm without converting.
2
Believing the frequency changes when a wave changes medium – it stays the same.
3
Thinking a bigger amplitude means a faster wave.
4
Using the wave speed in air for light.
5
Rearranging wrongly to λ = f / v.

Last updated: