كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme C — Wave Behaviour

Theme C — Wave Behaviour — IB Physics HL Revision Notes & Topical Questions

10 min read 13 parts Lesson 1 of 37 Unit quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

Theme C — Wave Behaviour — IB PHYSICS HL notes: Summarise simple harmonic motion, wave properties, refraction, diffraction, interference, standing waves and the Doppler effect for IB Physics HL.SHM — oscillation in which the acceleration is proportional to the displacement from e…

Amplitude x0
Period and frequency
Angular frequency
Restoring force
Total energy
Potential energy

Part 1 of 11Simple harmonic motion

1SHM

SHM oscillation in which the acceleration is proportional to the displacement from equilibrium and always directed towards it
a = −ω²x
What the symbols mean: a = acceleration (m s⁻²) · ω = angular frequency (rad s⁻¹) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre

2Amplitude x0

Amplitude x0 the maximum displacement

3Period and frequency

T is the time for one cycle and f = 1/T

4Angular frequency

ω = 2πf = 2π/T
What the symbols mean: ω = angular frequency (rad s⁻¹) · f = frequency (Hz) · T = period (s)

5Restoring force

F = −mω²x so a mass on a spring has k = mω²

6Phase

Phase x = x₀ sin(ωt + φ) where the phase angle φ fixes the starting point of the motion

Part 2 of 11Energy in SHM

Total energy

E_T = ½kx₀² = ½mω²x₀²
It is constant for an ideal system

Potential energy

E_P is zero at the centre and equals E_T at x = ±x₀

Kinetic energy

E_K is zero at x = ±x₀ and greatest at the centre
The two energy curves cross at half of E_T

Against time

E_K and E_P are squared sinusoids in antiphase with half the period of the motion
The average of each over a cycle is E_T/2

Speed at a position

E_K = E_T − E_P then v = √(2E_K/m)

Damping

Damping friction and air resistance transfer energy to thermal energy so the amplitude decays
Since E_T ∝ x₀², a 10% fall in amplitude per cycle is about a 19% fall in energy

Part 3 of 11The wave model

Wave

Wave transfers energy without transferring matter
Particles oscillate about fixed positions

Transverse wave

Transverse wave oscillation is perpendicular to the direction of travel

Longitudinal wave

Longitudinal wave oscillation is parallel to the direction of travel, giving compressions and rarefactions

Wavelength

Wavelength the distance between neighbouring points that are in phase

Wave equation

Wave equation v = fλ for all waves

Part 4 of 11Sound

Nature

Nature a longitudinal mechanical wave that cannot travel through a vacuum

Speed

Speed about 340 m s⁻¹ in air at 20 °C, 1500 m s⁻¹ in water and 5000 m s⁻¹ in steel
In a gas it rises with temperature and does not depend on pressure at fixed temperature

Pitch

Pitch set by frequency, with human hearing about 20 Hz to 20 kHz

Loudness

Loudness related to amplitude and intensity, I ∝ amplitude², where intensity is power per unit area in W m⁻²

Quality (timbre)

Quality (timbre) depends on the mixture of overtones present

Echo

Echo distinct if the delay exceeds about 0.1 s
The distance to a reflector is d = vt/2

Sonar and ultrasound

Sonar and ultrasound short wavelength resolves fine detail

Part 5 of 11Refraction and total internal reflection

1Refraction

Refraction when a wave enters a medium where its speed changes, the frequency stays constant while speed and wavelength change

2Refractive index

Refractive index n = c/v
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)

3Snell's law

Snell's law n₁ sin θ₁ = n₂ sin θ₂ with angles measured from the normal

4Total internal reflection

Total internal reflection needs light going from a denser to a less dense medium and an angle of incidence above the critical angle
sin c = n₂/n₁

5Critical angle

Critical angle at c the refracted ray travels along the boundary

6Reflection

Reflection a smooth surface gives specular reflection while a rough surface scatters light

Part 6 of 11Diffraction

Diffraction

Diffraction the spreading of a wave as it passes through a gap or around an obstacle
Wavelength, frequency and speed are unchanged

Size of effect

Size of effect greatest when the gap is about the same size as the wavelength
A narrower slit or a longer wavelength gives more spreading

Single slit

Single slit the first minimum is at θ = λ/b in radians for slit width b
The central maximum is by far the brightest and its angular width is 2λ/b

Low-frequency sound

Low-frequency sound diffracts around corners much more than high-frequency sound

Part 7 of 11Two-source interference

Two-source interference

Superposition

Superposition waves from two coherent sources overlap and their displacements add

Path difference

Path difference the difference in distance travelled to a point

Constructive interference

Constructive interference path difference nλ gives a bright fringe

Destructive interference

Destructive interference path difference (n + ½)λ gives a dark fringe

Central fringe

Central fringe the path difference is zero so it is bright

Double slits

Double slits bright fringes where nλ = d sin θ
Fringe spacing s = λD/d for small angles and D much greater than d

Dependence

Dependence fringes are wider for longer wavelength, larger D or closer slits

White light

White light a white central fringe with coloured outer fringes, blue inside and red outside

Envelope

Envelope each slit's single-slit pattern reduces the fringe intensity away from the centre
A fringe is missing where an interference maximum meets a diffraction minimum

Part 8 of 11Standing waves and harmonics

Formation

Formation two waves of equal amplitude and frequency travel in opposite directions

Nodes

Nodes points of permanent zero displacement where the waves are in antiphase

Antinodes

Antinodes points of maximum amplitude, up to twice that of either wave, where the waves are in phase

Spacing

Spacing adjacent nodes are λ/2 apart and a node and neighbouring antinode are λ/4 apart

Feature	Travelling wave	Standing wave
Energy	Transferred along the medium	Not transferred, stored in oscillations
Amplitude	Same for all points	Zero at nodes to maximum at antinodes
Phase	Changes steadily along the wave	Same within a segment, opposite in neighbouring segments
Wavelength	Distance between points in phase	Twice the distance between adjacent nodes

1String fixed at both ends or pipe open at both ends

String fixed at both ends or pipe open at both ends f₁ = v/2L and all harmonics occur, f_n = nf₁

2Pipe closed at one end

Pipe closed at one end f₁ = v/4L and only odd harmonics occur

3First overtone

First overtone the second harmonic in a string or open pipe but the third harmonic in a closed pipe

4Resonance tube

Resonance tube resonance when the air column is λ/4, 3λ/4 and so on
The difference between successive lengths is λ/2, which cancels the end correction

Part 9 of 11The Doppler effect

Moving source

Moving source wavefronts ahead bunch together and spread out behind
- (shorter wavelength, higher frequency)
The wave speed in the medium is unchanged

Moving observer

Moving observer an observer moving towards a stationary source crosses wavefronts more often so the observed frequency rises

Light and low speeds

Δλ/λ ≈ v/c

Spectral lines

Spectral lines lines shifted to longer wavelengths (red shift) show the source is receding
Opposite shifts from the two sides of a galaxy reveal rotation

Part 10 of 11Hubble's law and the age of the universe

Hubble's law

Hubble's law galaxies recede at speeds proportional to distance, v = H₀d
What the symbols mean: v = recession speed of the galaxy (km s⁻¹) · H₀ = Hubble constant (km s⁻¹ Mpc⁻¹) · d = distance (Mpc)
H₀ is about 70 km s⁻¹ Mpc⁻¹

Graph

Graph v against d is a straight line through the origin with gradient H₀

Expansion

Expansion the pattern is due to the expansion of space itself, so no galaxy is at the centre
Light is stretched too (cosmological redshift)

Hubble time

Hubble time t = 1/H₀ = 4.3 × 10¹⁷ s, about 13.8 billion years
This approximates the age of the universe and supports the Big Bang model

Part 11 of 11More from the specification

Simple Pendulum Restoring Force

In a simple pendulum, the restoring force is the tangential component of gravitational force.
- (F = -mg sin θ ≈ -mg x/L)

Kinematic Graphs of SHM

Graphs of displacement, velocity,
and acceleration against time show sinusoidal waveforms;
- velocity is the gradient of displacement, shifted by π/2 radians.

Phase Relations and Negative Sine/Cosine Graphs

If displacement starts at maximum amplitude (x = A cos ωt), velocity follows a negative sine curve and acceleration follows a negative cosine curve (a = -ω² x).

Mass-Spring Systems in Horizontal vs Vertical Planes

A horizontal mass-spring oscillator vibrates without gravitational influence,
while vertical oscillations occur about an equilibrium position where spring tension balances gravity.

Simple Pendulum Restoring Force

In a simple pendulum, the restoring force is the tangential component of gravitational force.
- (F = -mg sin θ ≈ -mg x/L)

Kinematic Graphs of SHM

Graphs of displacement, velocity,
and acceleration against time show sinusoidal waveforms;
- velocity is the gradient of displacement, shifted by π/2 radians.

Phase Relations and Negative Sine/Cosine Graphs

If displacement starts at maximum amplitude (x = A cos ωt), velocity follows a negative sine curve and acceleration follows a negative cosine curve (a = -ω² x).

Mass-Spring Systems in Horizontal vs Vertical Planes

A horizontal mass-spring oscillator vibrates without gravitational influence,
while vertical oscillations occur about an equilibrium position where spring tension balances gravity.

Pendulum

A weight swinging on a string, exchanging GPE and KE.

Velocity

Rate of change of displacement.

Simple pendulum

A small bob on a light string of length L

Gravitational potential

Work done per unit mass in bringing a test mass from infinity to the point.

Displacement-time graph

A graph of displacement against time whose gradient is velocity.

Velocity-time graph

A graph of velocity against time whose gradient is acceleration and area is displacement.

Key terms

Term	Meaning
Amplitude	The maximum displacement from the equilibrium position.
Restoring force	A force directed towards equilibrium and proportional to displacement in SHM, F = −mω²x.
Path difference	The difference in distance travelled by two waves from their sources to a point.
Critical angle	The angle of incidence in the denser medium that gives a 90° angle of refraction.
Node	A point of permanent zero displacement in a standing wave.
Antinode	A point of maximum amplitude in a standing wave.
Hubble constant	The constant of proportionality H₀ between recession speed and distance, v = H₀d.
Fringe separation	The distance between adjacent bright fringes, s = λD/d.

Avoid these mistakes

Saying a wider slit gives a wider diffraction pattern — it gives a narrower pattern because θ = λ/b.

Quoting λ/b as the full width of the central maximum — the full angular width is 2λ/b, and θ = λ/b needs radians.

Confusing slit width b with slit separation d, or assuming all double-slit maxima are equally bright.

Saying the wave carries particles along or that sound travels in a vacuum — particles only oscillate about fixed positions and sound needs a medium.

Confusing harmonics with overtones, or using the open-pipe formula for a closed pipe.

Last updated: 15 October 2026