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

C.1.1 Describing Oscillations — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 3 of 37 1 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

C.1.1 Describing Oscillations — IB PHYSICS SL notes: Describe an oscillation using displacement, amplitude, period, frequency, angular frequency and phase, and read these from a graph.Oscillation — the repetitive variation with time of the displacement x of an object about its eq…

Equilibrium position
Restoring behaviour
Properties
Displacement (x)
Amplitude (x0)
Time period (T)

Part 1 of 9What an oscillation is

Oscillation

Oscillation the repetitive variation with time of the displacement x of an object about its equilibrium position
Examples are a pendulum bob, a mass on a spring, a vibrating guitar string and atoms in a solid.

Equilibrium position

Equilibrium position the fixed central point (x = 0) where no resultant force acts on the object

Restoring behaviour

Restoring behaviour a displaced object always accelerates back towards equilibrium

Properties

Properties displacement, amplitude, time period, frequency and angular frequency describe the motion

Part 2 of 9Displacement and amplitude

Displacement (x)

Displacement (x) the distance of the object from equilibrium in a stated direction
It is a vector, so it can be positive or negative depending on the side of equilibrium.
It is measured in metres.

Amplitude (x0)

Amplitude (x0) the maximum displacement on either side of equilibrium
It is a positive scalar measured in metres.
A swing 8.0 cm either side of the centre has amplitude 8.0 cm, while the peak-to-peak range is 2x₀.

Part 3 of 9Period and frequency

Time period (T)

Time period (T) the time for one complete oscillation, in seconds
It is measured between two successive identical states of the motion.
If the period is constant the oscillation is isochronous.

Frequency (f)

Frequency (f) the number of oscillations per second, in hertz
f = 1/T
What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
1 Hz = 1 s⁻¹.

Part 4 of 9Angular frequency

1Angular frequency (ω)

Angular frequency (ω) the rate of change of angular displacement with time, in rad s⁻¹
ω = 2π/T = 2πf
What the symbols mean: ω = angular frequency (rad s⁻¹) · f = frequency (Hz) · T = period (s)
2π is the angle of one full circle.

2Link to circular motion

Link to circular motion one oscillation corresponds to an angle of 2π radians
From x = −A to equilibrium the angular displacement is π/2.
From equilibrium to the other extreme it is another π/2.
The whole return journey adds π, so one oscillation is 2π in total.

3Partial cycles

Partial cycles a half oscillation corresponds to an angle of π, so ω = π/t for that time t

4Calculator

Calculator it must be in radian mode when using ω

Part 5 of 9Displacement–time graphs

Amplitude

Amplitude read it as the maximum height of the curve above the axis

Period

Period read it as the horizontal distance between successive peaks or any two matching points
Draw arrows from the top of one peak to the top of the next, not between a trough and a peak.
Divide the total time by the number of cycles shown, so 3.5 cycles in 1.4 s gives T = 0.40 s.

Rest and fastest motion

Rest and fastest motion the object is at rest at the peaks and troughs and fastest where the curve crosses the axis

Velocity

Velocity it is the gradient of the displacement–time curve at that time

Other graphs

Other graphs velocity and acceleration graphs have the same period as the displacement graph

Part 6 of 9Phase and phase difference

1Phase

Phase it states which part of the cycle the object is in

2In phase

In phase two oscillators in step have phase difference 0

3Antiphase

Antiphase two oscillators exactly opposite have phase difference π rad (180°)

4Phase difference

Phase difference if one oscillator reaches its maximum a time ∆t after the other, ∆φ = 2π∆t/T
In degrees, ∆φ = 360° × ∆t/T.

5Condition

Condition a phase difference is meaningful only for oscillations of the same frequency

Part 7 of 9Free and damped oscillations

Ideal oscillation

Ideal oscillation with no energy loss it repeats indefinitely with constant amplitude

Damping

Damping friction and air resistance remove energy, so the amplitude decreases
Light damping leaves the period almost unchanged.

Driven oscillation

Driven oscillation a clock pendulum is kept going by energy supplied from a mechanism

Part 8 of 9Measuring the period

Measuring the period

Time many complete oscillations with a stopwatch.

Divide the total time by the number of oscillations to find T.

Take f = 1/T.

1Why many cycles

Why many cycles the timing error is shared over all cycles, so the percentage uncertainty in T is smaller

2Alternatives

Alternatives a data logger or motion sensor can plot displacement against time directly

Part 9 of 9More from the specification

1Simple Harmonic Motion (SHM) Definition

In simple harmonic motion, an oscillating system experiences an acceleration directly proportional and opposite to displacement from equilibrium, governed by the defining equation a = -ω²·x.

2Displacement-Time Graph of an Oscillator

A displacement-time graph for an SHM oscillator follows a sinusoidal curve (x = x₀ cos(ωt));
- the gradient at any point equals instantaneous velocity and reaches zero at maximum amplitude.

3Energy Interchange in Harmonic Oscillators

In both a mass-spring system and a simple pendulum in a gravitational field, mechanical energy continually exchanges between kinetic and potential energy stores,
where total energy is equal to ½·m·ω²·x₀².

4Simple pendulum

A small bob on a light string of length L

5Gravitational potential

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

6Displacement-time graph

A graph of displacement against time whose gradient is velocity.

7Velocity-time graph

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

8Harmonic

Resonant mode of a stationary wave, with frequency a whole-number multiple of the fundamental where allowed.

9Kinetic energy

K = ½mv², energy of motion.

10Potential energy

Energy stored by the configuration of a system.

Key terms

Term	Meaning
Equilibrium position	The position where the net force on the object is zero.
Displacement x	Distance from equilibrium in a given direction (vector).
Amplitude x₀	Maximum displacement from equilibrium.
Time period T	Time for one complete oscillation.
Frequency f	Number of oscillations per second, f = 1/T.
Angular frequency ω	2π/T, in radians per second.
Phase difference	Fraction of a cycle by which two oscillations are out of step, expressed as an angle.

Avoid these mistakes

Taking the amplitude to be the peak-to-peak distance — it is measured from equilibrium.

Using the number of cycles shown on a graph instead of the time for one cycle when finding T.

Forgetting that f = 1/T and ω = 2πf differ by a factor of 2π.

Saying displacement is always positive — it is a vector measured from equilibrium.

Calculating a phase difference between oscillations with different frequencies.

Last updated: 15 October 2026