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Wave properties — KCSE Physics

KCSE Physics · 132 practice questions · 9 syllabus objectives · 9 revision lessons

42 easy42 medium48 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Distinguish between progressive and stationary waves and state conditions for standing wave formation

Define wavelength, frequency, amplitude, period and wave speed; write the wave equation v = fλ

Distinguish between transverse and longitudinal waves and give examples of each

Apply v = fλ to calculate wave speed, frequency or wavelength from given data

Define a wave and explain how waves transfer energy without transferring matter

Distinguish between transverse and longitudinal waves, giving examples and sketching diagrams

Define wavelength, amplitude, frequency, period and derive/apply the wave equation v = fλ

Read wave parameters from displacement-distance and displacement-time graphs and sketch modified waveforms

Wave properties

Revision Notes

Concise lesson notes for Wave properties, written to the KCSE Physics marking standard. Read the first lesson free below.

Progressive vs Stationary Waves

Waves are essential in physics, and understanding their types is crucial. Progressive waves are waves that move through a medium, transferring energy from one point to another. They can be either longitudinal or transverse. Examples include sound waves and light waves.

In contrast, stationary waves (or standing waves) do not transfer energy; instead, they result from the interference of two progressive waves traveling in opposite directions.

Conditions for standing wave formation:

  • Two waves must have the same frequency.
  • They must travel in opposite directions.
  • They must have a constant amplitude.
  • They must be coherent, meaning they maintain a constant phase difference.

In stationary waves, nodes (points of no displacement) and antinodes (points of maximum displacement) are formed. This can be observed in a vibrating string fixed at both ends, where the waves reflect back and interfere with incoming waves, creating a standing wave pattern.

Key points to remember

  • Progressive waves transfer energy through a medium.
  • Stationary waves result from interference of two opposite waves.
  • Standing waves have nodes and antinodes.
  • Conditions: same frequency, opposite direction, constant amplitude.
  • Coherence is essential for standing wave formation.

Worked example

Distinguish between progressive and stationary waves.

  • Progressive waves transfer energy through a medium.
  • Stationary waves do not transfer energy but form nodes and antinodes.

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More lessons in this topic

Lesson 2: Key Wave Properties and the Wave Equation

Objective: Define wavelength, frequency, amplitude, period and wave speed; write the wave equation v = fλ

In physics, understanding wave properties is essential. Here are the key definitions:

  • Wavelength (λ): The distance between two consecutive crests or troughs in a wave. Measured in meters (m).
  • Frequency (f): The number of complete waves passing a point in one second. Measured in hertz (Hz).
  • Amplitude: The maximum displacement of a point on the wave from its rest position. Measured in meters (m).
  • Period (T): The time taken for one complete wave to pass a point. Measured in seconds (s).
  • Wave Speed (v): The speed at which the wave travels through a medium. Measured in meters per second (m/s).

The relationship between these properties is described by the wave equation: v = fλ, where:

  • v = wave speed
  • f = frequency
  • λ = wavelength

This equation allows us to calculate one property if the other two are known. For example, if the frequency of a wave is 5 Hz and the wavelength is 2 m, the wave speed can be calculated as follows: v = fλ = 5 Hz × 2 m = 10 m/s.

  • Wavelength is the distance between consecutive crests or troughs.
  • Frequency is the number of waves per second, measured in hertz.
  • Amplitude is the maximum displacement from the rest position.
  • Period is the time for one complete wave cycle.
  • Wave speed is calculated using v = fλ.

Calculate the wave speed if the frequency is 10 Hz and the wavelength is 0.5 m. Answer: v = fλ = 10 Hz × 0.5 m = 5 m/s.

Lesson 3: Transverse vs. Longitudinal Waves

Objective: Distinguish between transverse and longitudinal waves and give examples of each

Waves can be classified into two main types: transverse waves and longitudinal waves.

Transverse Waves: In these waves, the particle displacement is perpendicular to the direction of wave propagation. This means that as the wave travels, the particles move up and down. Common examples of transverse waves include:

  • Light waves
  • Waves on a string
  • Water waves (surface)

Longitudinal Waves: In longitudinal waves, the particle displacement is parallel to the direction of wave propagation. Here, particles compress and rarefy as the wave travels through. Examples of longitudinal waves include:

  • Sound waves in air
  • Pressure waves in fluids
  • Seismic P-waves

To summarize, the key difference lies in the direction of particle movement relative to wave direction. Transverse waves have perpendicular movement, while longitudinal waves have parallel movement.

  • Transverse waves have perpendicular particle displacement to wave direction.
  • Longitudinal waves have parallel particle displacement to wave direction.
  • Examples of transverse waves include light and water waves.
  • Examples of longitudinal waves include sound waves and seismic P-waves.
  • Understanding wave types is essential in physics applications.

Distinguish between transverse and longitudinal waves.

  • Transverse waves: particles move perpendicular to wave direction (e.g., light waves).
  • Longitudinal waves: particles move parallel to wave direction (e.g., sound waves).
Lesson 4: Calculating Wave Speed, Frequency, and Wavelength

Objective: Apply v = fλ to calculate wave speed, frequency or wavelength from given data

In wave physics, the relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the equation: v = fλ. Understanding this relationship allows us to calculate any one of these three properties if the other two are known.

  • Wave Speed (v): The speed at which the wave travels through a medium.
  • Frequency (f): The number of waves passing a point per second, measured in Hertz (Hz).
  • Wavelength (λ): The distance between successive crests (or troughs) of a wave, measured in meters (m).

To calculate the wave speed, rearrange the formula: v = f × λ. To find frequency, use f = v / λ. For wavelength, use λ = v / f.

For example, if a wave has a frequency of 10 Hz and a wavelength of 2 meters, the wave speed can be calculated as:

  • v = f × λ
  • v = 10 Hz × 2 m = 20 m/s

Thus, the wave speed is 20 m/s.

  • Wave speed (v) is calculated using v = fλ.
  • Frequency (f) is measured in Hertz (Hz).
  • Wavelength (λ) is measured in meters (m).
  • Rearrange v = fλ to find any unknown variable.
  • Example: v = 20 m/s if f = 10 Hz and λ = 2 m.

Calculate the wave speed if the frequency is 5 Hz and the wavelength is 3 m.

  • v = f × λ
  • v = 5 Hz × 3 m = 15 m/s

Sample Questions

Read 3 questions and answers free. Sign up to access all 132 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER4 marks

State the definitions of the following wave properties and their SI units: (a) wavelength (1 mark), (b) frequency (1 mark), (c) amplitude (1 mark), (d) period (1 mark).

Answer & marking scheme

Part (a) — 2 marks
Wavelength (λ) is the distance between two successive crests or troughs; SI unit: metre (m) (1 mk)
Part (b) — 2 marks
Frequency (f) is the number of cycles per second; SI unit: hertz (Hz) (1 mk)
Part (c) — 2 marks
Amplitude (A) is the maximum displacement from the rest position; SI unit: metre (m) (1 mk)
Part (d) — 2 marks
Period (T) is the time taken to complete one full cycle; SI unit: second (s) (1 mk)
2
easySHORT ANSWER4 marks

State the differences between transverse and longitudinal waves in terms of particle movement. (4 marks)

Answer & marking scheme

Part (a) — 4 marks
In transverse waves, particles move at right angles to the direction of wave propagation (1 mk)
In longitudinal waves, particles move parallel to the direction of wave propagation (1 mk)
Transverse waves can be seen in water and electromagnetic waves (1 mk)
Longitudinal waves can be observed in sound waves and compressions in a slinky (1 mk)
3
easySHORT ANSWER3 marks

A sound wave travels through air with a frequency of 440 Hz and a wavelength of 0.78 m. Calculate the speed of the sound wave using the formula v = fλ. (3 marks)

Answer & marking scheme

Part (a) — 3 marks
Wave speed (v) is calculated as v = f × λ (1 mk)
Substituting values: v = 440 Hz × 0.78 m (1 mk)
The calculated wave speed is 343.2 m/s (1 mk)
4

Identify the main differences between transverse and longitudinal waves and provide one example for each type. (4 marks)

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Frequently asked questions

What does the KCSE Physics topic "Wave properties" cover?

Wave properties covers Distinguish between progressive and stationary waves and state conditions for standing wave formation; Define wavelength, frequency, amplitude, period and wave speed; write the wave equation v = fλ; Distinguish between transverse and longitudinal waves and give examples of each, and more, all aligned to the official KNEC KCSE Physics syllabus.

How many practice questions are available for Wave properties?

HighMarks has 132 Wave properties practice questions for KCSE Physics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Physics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Wave properties for the KCSE exam?

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