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3.1.2Waves

The Wave Equation — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

5 min read 10 parts Lesson 4 of 35 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision
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Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
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Lesson summary

3.1.2 The Wave Equation — IGCSE PHYSICS notes: Use v = fλ and f = 1 ÷ T to link wave speed, frequency, wavelength and period.Equation — v = fλWhat the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)v is wave speed in metres per second (m/s)f is freq…

  • Both types
  • Rearranged
  • One period
  • Substitution
  • Crest to nearest trough
  • Constant speed

Part 1 of 8The wave equation

The wave equation
Equation
  • Equation v = fλ
    What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
  • v is wave speed in metres per second (m/s)
  • f is frequency in hertz (Hz)
  • λ is wavelength in metres (m)
Meaning
  • Meaning wave speed is the distance travelled by a wave each second and the speed at which energy transfers through a medium
Both types
  • Both types transverse and longitudinal waves obey it
Rearranged
  • Rearranged f = v ÷ λ and λ = v ÷ f

Part 2 of 8Where it comes from

One period
  • One period in one period T a wave travels exactly one wavelength λ
Speed
  • Speed v = distance ÷ time = λ ÷ T
Substitution
  • Substitution since f = 1 ÷ T this gives v = fλ

Part 3 of 8Frequency and period

Period
  • Period the time taken for one complete wave to pass a fixed point
Relation
  • Relation f = 1 ÷ T and T = 1 ÷ f
Units
  • Units f in hertz (Hz) and T in seconds (s)
Crest to nearest trough
  • Crest to nearest trough the distance is half a wavelength, so the wavelength is twice this distance

Part 4 of 8Method for calculations

1
Write down the known quantities with units.
2
Convert to SI units: kHz to Hz by × 1000, MHz to Hz by × 1 000 000, cm to m by ÷ 100, nm to m by × 10−9.
3
Write the equation and rearrange for the unknown.
4
Substitute and give the answer with a unit and suitable significant figures.
5
Check the size is sensible, for example sound of 500 Hz has a wavelength under a metre.

Part 5 of 8What changes and what stays the same

Frequency
  • Frequency set by the source and does not change when the wave crosses into another medium
Speed
  • Speed depends on the medium
Wavelength
  • Wavelength since v = fλ and f is fixed, wavelength changes in the same proportion as speed
  • A slower wave has a shorter wavelength
  • This is the basis of refraction
Constant speed
  • Constant speed in one medium f and λ are inversely proportional

Part 6 of 8Typical wave speeds

Sound in air
  • Sound in air about 340 m/s, and 330 m/s is also used
Light
  • Light all electromagnetic waves travel at 3.0 × 108 m/s in a vacuum
Water ripples in a tank
  • Water ripples in a tank less than 1 m/s

Part 7 of 8Graphs and echoes

Graphs and echoes
Graph of wavelength against 1 ÷ f
  • Graph of wavelength against 1 ÷ f a straight line through the origin whose gradient is v
Echo method
  • Echo method clap at a measured distance d from a wall and time the echo, which travels 2d
  • v = 2d ÷ t
  • Use a long distance and repeat to reduce timing error
Entering a new medium
  • Entering a new medium find f from the original data, keep it fixed, then use the new speed to find the new wavelength

Part 8 of 8More from the specification

1Wave speed and propagating crests
  • Wave speed and propagating crests multiplying frequency by wavelength determines the speed at which propagating wave crests travel through continuous media.
2Diffraction
  • Spreading of waves through a gap or around an edge
3Wavefront
  • Line joining points on a wave that are in step
4Reflection
  • Light bouncing off a surface.
5Spread
  • The extent to which repeated readings differ.
6Amplitude
  • Amplitude measured from the undisturbed rest position to a peak or trough, not from crest to trough.

Key terms

TermMeaning
Wave speedDistance travelled by a wave each second
Wave equationv = fλ
PeriodTime for one complete wave to pass a fixed point
HertzUnit of frequency, one wave per second
WavelengthDistance from a point on a wave to the same point on the next wave

Avoid these mistakes

1
Not converting units — 2.5 kHz is 2500 Hz and 40 cm is 0.40 m.
2
Using the wrong symbols — use v, f and λ, not L or W.
3
Forgetting that f is unchanged when a wave changes medium — find f first and keep it fixed.
4
Confusing crest-to-trough with a full wavelength — a full wavelength is crest to crest.

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