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.5.4 Equations for the Doppler Effect of Sound — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 37 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.5.4 Equations for the Doppler Effect of Sound — IB PHYSICS HL notes: Use the Doppler equations for a moving source and a moving observer of sound, including the wavelength form.Setting — the source moves with speed us relative to the air and the observer is stationaryEquation —…

Approaching
Wave speed
Source receding
Not symmetric
Direction check
Observer example form

Part 1 of 6Moving source, stationary observer

Setting

Setting the source moves with speed u_s relative to the air and the observer is stationary

Equation

Equation f′ = f v/(v ± u_s)

Approaching

Approaching the denominator is v − u_s so f′ is larger

Receding

Receding the denominator is v + u_s so f′ is smaller

Wave speed

Wave speed the speed of sound v is about 340 m s⁻¹ in air

Reason

Reason each wavefront is emitted from a position the source has moved to

Part 2 of 6Moving observer, stationary source

Setting

Setting the source is stationary and the observer moves with speed u_o

Equation

Equation f′ = f (v ± u_o)/v

Approaching

Approaching the numerator is v + u_o so f′ is larger

Receding

Receding the numerator is v − u_o so f′ is smaller

Wavelength

λ = v/f is unchanged but the waves pass the observer at relative speed v ± u_o

Part 3 of 6Wavelength form

Moving source

λ′ = λ(1 ∓ u_s/v)

Source approaching

Source approaching the bracket is 1 − u_s/v, so the wavelength shortens

Source receding

Source receding the bracket is 1 + u_s/v, so the wavelength lengthens

Link

Link f′ = v/λ′

Part 4 of 6Choosing the equation

Moving source

Moving source use the denominator form

Moving observer

Moving observer use the numerator form

Not symmetric

Not symmetric equal speeds give nearly equal shifts only when u is much smaller than v

Direction check

Direction check an approaching source or observer must give f′ greater than f

Medium

Medium speeds are measured relative to the air and not relative to each other

Labelling

Labelling mark source and observer on the diagram to choose the sign correctly

Part 5 of 6Finding a speed from a frequency

Identify whether the source or the observer moves.

Write the correct equation and the sign for approach or recession.

Rearrange to make the speed the subject.

Substitute f, f′ and v.

Check that the sign of the change matches the direction.

Observer example form

Observer example form u_o = v(1 − f′/f) for an observer moving away from a stationary source of frequency f who hears f′

Quick check

Quick check a small shift gives Δf/f ≈ u/v

Part 6 of 6More from the specification

1Acoustic Doppler frequency calculation

Acoustic Doppler frequency calculation calculating relative velocities between sound sources and moving observers provides an exact mathematical means for frequency shifts.

2The Doppler Effect and Wavelength Shift

When a source of sound or light moves relative to an observer, the observed wavelength shifts;
- moving towards the observer causes wavefronts to bunch together, decreasing wavelength (blueshift),
while moving away stretches wavefronts,
increasing wavelength (redshift).

3Cosmological Redshift of Distant Galaxies

Light emitted from distant galaxies observed from Earth shows absorption lines shifted towards the red end of the spectrum compared to laboratory reference values;
- this redshift indicates that distant galaxies are receding with radial velocity v.

4Redshift Equation and Hubble's Law

The fractional change in wavelength for an astronomical object moving at non-relativistic velocity v is given by z = Δλ / λ₀ ≈ v / c;
- Hubble's law (v = H₀·d) uses this recessional velocity to determine distances across the expanding universe.

5Galaxy

Huge group of stars, gas, dust and solar systems held by gravity.

6Redshift

Increase in the wavelength of light from a source moving away from the observer.

7Spectrum

Range of colours in white light.

8Velocity

Rate of change of displacement.

9Constant

Not changing.

10Electromagnetic wave

Transverse wave that transfers energy from a source to an absorber

11Galactic redshift

Shift of galaxy spectral lines to longer wavelength due to recession.

12Spectral lines

Dark or bright lines in a spectrum at wavelengths characteristic of elements.

Key terms

Term	Meaning
Observed frequency (f′)	The frequency detected by the observer.
Source speed (u_s)	The speed of the source relative to the air.
Observer speed (u_o)	The speed of the observer relative to the air.
Wave speed (v)	The speed of sound in the medium.

Avoid these mistakes

Adding instead of subtracting in the denominator for an approaching source.

Using the speed relative to the observer instead of the speed relative to the medium.

Applying the source formula to a moving observer.

Getting the direction of change wrong — approach must give f′ > f.

Last updated: 15 October 2026

Cambridge 9702 & Edexcel Physics Mark Scheme Points

Doppler Shift & Galactic Red-shift Criteria

Key Equation: Δλ / λ ≈ Δf / f ≈ v / c

Red-shift: Fractional increase in observed wavelength from receding galaxies.
Hubble's Law: v = H₀d (Universe age ≈ 1 / H₀).
Evidence for Big Bang: Cosmological red-shift + CMBR at 2.7K.