IB DP Physics: Travelling waves and the Doppler effect (DP Physics) – Revision Notes

These notes condense sub-topics C.2 (Wave model) and C.5 (Doppler effect) from the IB Physics guide (first assessment 2025) into one page for the final weeks. C.2 and most of C.5 are SL and HL. The Doppler formulas for sound and other mechanical waves are additional higher level, so they are marked HL only. Full explanations and worked examples are in the study guide. When you are ready to test yourself, use the practice questions and the free 10-minute diagnostics.

Related pages: the course hub, the printable checklist and kinematics revision notes.

C.2 Wave model

Definitions

• Travelling wave: a disturbance that transfers energy through a medium or space. The medium as a whole is not shifted.
• Transverse: particle oscillation is at right angles to the direction of travel.
• Longitudinal: particle oscillation is along the line of travel, forming compressions and rarefactions.
• Wavelength λ: distance between neighbouring points in phase.
• Frequency f: oscillations per second, in hertz.
• Time period T: time for one oscillation, T = 1/f.
• Wave speed v: speed of the pattern.

Formulas

Quantity	Relationship	Notes
Wave speed	v = fλ = λ/T	Any wave
Period	T = 1/f	Seconds and hertz
EM waves in a vacuum	c = fλ	c = 3.00 × 10⁸ m s⁻¹ for every EM wave
New medium	f unchanged, λ ∝ v	Source sets f, medium sets v

Method: wave speed problems

1. Convert to base units (m, s, Hz). Change kHz, MHz, GHz and nm first.
2. Choose the relationship that matches the data: v = fλ if you have f, v = λ/T if you have T.
3. Rearrange before substituting.
4. Give the answer with a unit and to the number of significant figures in the data.

Sound and electromagnetic waves

Feature	Sound	Electromagnetic
Wave type	Longitudinal	Transverse
Medium	Required	Not required
Speed	Depends on the medium	c in a vacuum for all
What oscillates	Air (or other) particles	Electric and magnetic fields, perpendicular to each other

Mechanical waves need a medium and can be transverse or longitudinal. Electromagnetic waves do not need a medium and are always transverse.

Orders of magnitude of wavelength (rough)

Region	Wavelength
Radio	10⁻¹ m and longer
Microwave	10⁻³ to 10⁻¹ m
Infrared	10⁻⁶ to 10⁻³ m
Visible	about 4 × 10⁻⁷ to 7 × 10⁻⁷ m
Ultraviolet	10⁻⁸ to 10⁻⁷ m
X-ray	10⁻¹¹ to 10⁻⁸ m
Gamma ray	10⁻¹² m and shorter

Order from long to short wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. The order of frequency is the reverse.

Method: particle motion from a graph

1. Identify the direction of travel of the wave.
2. For a displacement-position graph, move the whole profile a small distance in that direction.
3. Compare the new value at the particle with its old one. Higher means moving up (or forward); lower means moving down (or backward).
4. For a longitudinal wave, a compression is at a point of zero displacement where the particles on either side are displaced towards it. A rarefaction is at zero displacement where they are displaced away.
5. A particle at maximum displacement is momentarily at rest. A particle at zero displacement is moving at its greatest speed.

C.5 Doppler effect

Key ideas

• The Doppler effect is the change in observed frequency (and wavelength) when source and observer have relative motion.
• Source moving: wavefronts bunch up in front (shorter λ, higher f) and spread out behind (longer λ, lower f). The wave speed in the medium does not change.
• Observer moving: the wavefronts keep equal spacing and λ is unchanged. The observer meets them more often when approaching (higher f) and less often when receding (lower f).
• Closing means higher frequency and blueshift. Separating means lower frequency and redshift.

Light (SL and HL)

When the relative speed v is much smaller than c:

Δf/f = Δλ/λ ≈ v/c

Symbol	Meaning
Δλ	Observed wavelength minus rest wavelength
λ	Rest wavelength of the line
v	Relative speed along the line of sight
c	3.00 × 10⁸ m s⁻¹

Method: find Δλ, divide by λ, multiply by c. A positive Δλ means redshift and recession.

Spectral lines: compare a star’s or galaxy’s lines with the laboratory wavelengths. The direction and size of the shift give the line-of-sight velocity. A repeating back-and-forth shift suggests orbital motion.

HL only: sound and mechanical waves

Case	Formula	Sign rule
Moving source, us	f′ = f v/(v ± us)	v − us towards the observer; v + us away
Moving observer, uo	f′ = f(v ± uo)/v	v + uo towards the source; v − uo away

Never both moving. Wavelength from a moving source: λ′ = (v − us)/f in front of it and (v + us)/f behind it.

Method to find a speed: write the formula with the signs chosen from the situation, rearrange for us or uo, then substitute. Check that the answer is smaller than v.

Medical and radar uses

• Doppler ultrasound: the echo from moving blood is shifted in frequency, which gives the speed and direction of flow.
• Radar speed checks: microwaves reflect from a moving vehicle with a shift that increases with its speed.

Worked reminders

Wave on a string. A wave of period 0.125 s has wavelength 0.90 m. Then v = λ/T = 0.90/0.125 = 7.2 m s⁻¹ and f = 1/T = 8.0 Hz.

Colour of light. A red laser emits at 4.5 × 10¹⁴ Hz. Then λ = c/f = 3.00 × 10⁸ / 4.5 × 10¹⁴ = 6.7 × 10⁻⁷ m, which lies in the visible band.

Sign check for HL. A source of 300 Hz recedes at 17 m s⁻¹ with v = 340 m s⁻¹. Receding means a lower frequency, so use v + us: f′ = 300 × 340/357 = 286 Hz. This is below 300 Hz, as it should be.

Must-know distinctions

• Transverse against longitudinal: direction of oscillation relative to travel, not the speed or the medium.
• Wave speed against particle speed: the pattern travels at v, while particles oscillate and keep changing speed.
• Moving source against moving observer: only the source changes the wavelength.
• Light against sound: for light you use Δf/f ≈ v/c. For sound the HL formulas depend on motion relative to the medium.
• Frequency against wavelength at a boundary: frequency stays the same, wavelength changes with speed.

Quick self-test

1. A wave has frequency 50 Hz. What is its period?
2. A sound wave in air has wavelength 0.34 m and speed 340 m s⁻¹. Find its frequency.
3. A wave of frequency 6.0 Hz and wavelength 0.25 m travels along a spring. Find its speed.
4. A 1.5 GHz microwave signal travels in air. Find its wavelength, using c = 3.00 × 10⁸ m s⁻¹.
5. Sound passes from air into water. Which of f, λ and v change?
6. On a displacement-position graph for a longitudinal wave, where is a compression?
7. A spectral line of rest wavelength 393.4 nm is observed at 393.9 nm. Find the speed along the line of sight and say if the source approaches or recedes.
8. Name the region of the electromagnetic spectrum with wavelengths of about 10⁻¹⁰ m.
9. (HL only) A 600 Hz source moves towards you at 20 m s⁻¹. Take v = 340 m s⁻¹. Find f′.
10. (HL only) An observer moves away from a stationary 500 Hz source at 10 m s⁻¹. Take v = 330 m s⁻¹. Find f′.
11. (HL only) A source of 500 Hz is heard at 540 Hz as it approaches. Take v = 340 m s⁻¹. Find us.
12. State one medical use of the Doppler effect.

Answers

1. T = 1/50 = 0.020 s.
2. f = v/λ = 340/0.34 = 1000 Hz.
3. v = fλ = 6.0 × 0.25 = 1.5 m s⁻¹.
4. λ = c/f = 3.00 × 10⁸ / 1.5 × 10⁹ = 0.20 m.
5. The frequency does not change. The speed and wavelength both change.
6. At a point of zero displacement where the particles on either side are displaced towards it.
7. Δλ = 0.5 nm, so v = 3.00 × 10⁸ × 0.5/393.4 = 3.8 × 10⁵ m s⁻¹. The wavelength has increased, so the source recedes.
8. X-rays (within the X-ray band, from about 10⁻¹¹ to 10⁻⁸ m).
9. f′ = 600 × 340/(340 − 20) = 600 × 340/320 = 638 Hz.
10. f′ = 500 × (330 − 10)/330 = 485 Hz.
11. 540 = 500 × 340/(340 − us), so 340 − us = 500 × 340/540 = 314.8 and us = 25.2 m s⁻¹.
12. Doppler ultrasound measures the speed of blood flow from the frequency shift of echoes.

Where marks are usually lost

• Leaving frequencies in MHz or wavelengths in nm when substituting into v = fλ.
• Describing particles as carried forward by the wave instead of vibrating about their rest positions.
• Putting a compression at maximum displacement.
• Saying the frequency changes when a wave enters a new medium.
• Giving a Doppler explanation that changes the wave speed, when for a moving source it is the wavelength that changes.
• Using Δλ/λ ≈ v/c with the wrong wavelength in the denominator. Use the rest wavelength.
• Missing the direction: a redshift means moving away, and you should say so.
• Choosing the wrong sign in v ± us or v ± uo. Test it: towards must give a higher frequency.
• Giving a speed with no unit, or more significant figures than the data allow.

Official syllabus

Source: Physics guide, first assessment 2025, International Baccalaureate Organization (Diploma Programme), sub-topics C.2 Wave model and C.5 Doppler effect.