ما هي العلاقة بين سرعة الموجة وترددها؟ وما هو تأثير دوبلر؟ What is the wave equation and Doppler effect?

المعادلة العامة للموجات هي v = fλ (حيث v السرعة بـ m/s، f التردد بالهرتز، λ الطول الموجي بالمتر). وتأثير دوبلر هو التغير الظاهري في تردد الموجة نتيجة الحركة النسبية بين المصدر والمراقب: f_obs = f(v ± v_o)/(v ∓ v_s). [الصيغة الرمزية الموزونة: v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f]

Theme C — Wave Behaviour

C.3 Wave Phenomena — IB Physics HL Revision Notes & Topical Questions

5 min read 12 parts Lesson 16 of 37 1 quiz

📚 IB Physics HL Hub / Topical Revision

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

C.3 Wave Phenomena — IB PHYSICS HL notes: Describe wavefronts and rays, reflection, refraction, diffraction, superposition, interference, Young's double slit, single-slit diffraction and diffraction gratings.Wavefront — a line or surface joining points that oscillate in phaseIt i…

Surface waves
Spherical waves
Possible outcomes
Law of reflection
During reflection
Transmission

Part 1 of 9Wavefronts and rays

Wavefront

Wavefront a line or surface joining points that oscillate in phase
It is perpendicular to the direction of motion and energy transfer

Ray

Ray a line showing the direction of energy transfer, perpendicular to the wavefront

Surface waves

Surface waves two-dimensional with circular wavefronts

Spherical waves

Spherical waves three-dimensional such as sound or light, with spherical wavefronts

Spacing

Spacing the distance between successive peak wavefronts equals the wavelength

Part 2 of 9Reflection and transmission

Reflection and transmission

Possible outcomes

Possible outcomes at a boundary a wave can be reflected, refracted, transmitted or absorbed

Law of reflection

Law of reflection angle of incidence i = angle of reflection r, measured from the normal

During reflection

During reflection frequency, wavelength and speed do not change

Transmission

Transmission a wave appears on the other side of the boundary
Refraction is transmission with a change of direction

Absorption

Absorption a transmitted wave has a lower amplitude if some absorption occurs

Wave types

Wave types these behaviours occur for both transverse and longitudinal waves

Part 3 of 9Refraction and Snell's law

1Refraction

Refraction the change in direction of a wave when it crosses a boundary between media of different optical density, caused by a change in speed

2Entering a denser medium

Entering a denser medium the wave slows, the wavelength shortens and it bends towards the normal

3Entering a less dense medium

Entering a less dense medium the wave speeds up, the wavelength lengthens and it bends away from the normal

4Unchanged quantity

Unchanged quantity the frequency stays the same, so the colour does not change

5Along the normal

Along the normal a wave incident at 90° passes straight through without changing direction

6Water waves

Water waves they slow and their wavelength shortens when going from deep to shallow water

7Refractive index

Refractive index n = c/v, a dimensionless ratio that is 1 for air and above 1 for denser media
What the symbols mean: n = refractive index (no unit) · c = speed of light in a vacuum (3.00 × 10⁸ m s⁻¹) · v = speed of light in the material (m s⁻¹)

8Snell's law

Snell's law n₁ sin θ₁ = n₂ sin θ₂ and n₂/n₁ = v₁/v₂

Part 4 of 9Critical angle and total internal reflection

Critical angle c

Critical angle c the angle of incidence in the denser medium that gives an angle of refraction of 90°
sin c = n₂/n₁

Size

Size a larger refractive index gives a smaller critical angle

Below c

Below c the ray is refracted out of the material

Above c

Above c the ray undergoes total internal reflection, obeying the law of reflection

Conditions

Conditions n₂ < n₁ and angle of incidence greater than c

Use

Use optical fibres

Part 5 of 9Diffraction

Definition

Definition the spreading out of waves after passing through a narrow gap or around an obstruction

Most noticeable

Most noticeable when the wavelength and gap width are similar
A much bigger gap gives little diffraction

Through a gap

Through a gap the waves curve and their amplitude is lower

Around a barrier

Around a barrier the larger the wavelength, the greater the diffraction and the smaller the shadow

Constant quantities

Constant quantities wavelength, frequency and speed are unchanged

Examples

Examples radio waves around buildings, X-rays through crystals and sound through a doorway

Part 6 of 9Superposition and coherence

Superposition and coherence

Principle

Principle where waves overlap the resultant displacement is the sum of the individual displacements, treated as vectors

Pulses

Pulses pulses pass through each other unchanged after overlapping

Interference

Interference the effect of superposition

Coherent sources

Coherent sources they have the same frequency and a constant phase difference

Constructive interference

Constructive interference waves in phase give a larger resultant amplitude

Destructive interference

Destructive interference waves in antiphase cancel

Examples

Examples monochromatic laser light and two loudspeakers emitting one frequency

Part 7 of 9Path difference and interference conditions

Path difference

Path difference the difference in distance travelled by two waves from their sources to the point where they meet

Constructive

Constructive path difference = nλ

Destructive

Destructive path difference = (n + ½)λ

Order n

Order n n = 0, 1, 2, … with n = 0 the central position

Feature	Constructive	Destructive
Path difference (sources in phase)	nλ	(n + ½)λ
Phase difference	0, 2π, 4π …	π, 3π …
Resultant amplitude	Maximum	Minimum
Light pattern	Bright fringe	Dark fringe

Part 8 of 9Single-slit diffraction (HL)

1Pattern

Pattern a wide bright central maximum with much narrower, dimmer maxima on either side

2Huygens principle

Huygens principle each point of the wavefront acts as a source of coherent wavelets

3First minimum

θ = λ/b in radians, from b sin θ = λ
Further minima occur at b sin θ = nλ

4Width

Width the central maximum has angular width 2λ/b and linear width 2λD/b

5Wavelength

Wavelength a longer wavelength gives a wider pattern, red wider than blue

6Slit width

Slit width a narrower slit gives a wider pattern

Part 9 of 9Double-slit modulation and diffraction gratings (HL)

Modulation

Modulation the double-slit fringes lie inside the single-slit intensity envelope

Grating

Grating many very thin equally spaced parallel slits
Slit spacing d = 1/N from N lines per metre

Grating equation

Grating equation nλ = d sin θ with n the order

More slits

More slits maxima are narrower and brighter with wider dark regions

Highest order

Highest order n_max = d/λ rounded down

White light

White light a white central maximum and spectra in other orders, violet nearest the centre and red furthest

Key terms

Term	Meaning
Wavefront	A surface joining points on a wave that are in phase.
Ray	A line showing the direction of energy transfer, perpendicular to wavefronts.
Refractive index	The ratio of the speed of light in a vacuum to its speed in the medium.
Critical angle	The angle of incidence in the denser medium for which the angle of refraction is 90°.
Diffraction	The spreading of a wave as it passes through an aperture or round an obstacle.
Coherent sources	Sources with a constant phase difference.
Path difference	The difference in distance travelled by two waves from their sources to a point.
Diffraction grating	A large number of equally spaced parallel slits that produce sharp interference maxima.

Avoid these mistakes

Saying frequency changes on refraction — it stays the same.

Confusing path difference with the distance between the sources.

Mixing up the slit separation d, the slit width b and the screen distance D.

Measuring angles from the boundary instead of the normal in Snell's law.

Rounding d/λ up instead of down for the maximum order.

Last updated: 13 October 2026