Wave speed, frequency and wavelength

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課程筆記

Big idea: wave speed, frequency and wavelength

Key concept: Relationships. Wave speed equals frequency times wavelength. Waves transfer energy without a net transfer of the medium through the whole wave journey.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Wave relationships help explain sound, light and communications.

Wave Basics & Energy Transfer

Waves transfer energy without transferring matter.
Objects floating on water bob up and down but do not move with the wave – evidence that matter is not transferred.
Waves are described as oscillations or vibrations about a fixed point.
Ripples cause water particles to oscillate up and down; sound waves cause air particles to vibrate back and forth.

A toy duck bobbing up and down on water waves, illustrating that waves transfer energy but not matter.

Features of a Wave

Amplitude – maximum displacement from undisturbed position; measured in metres (m).
Wavelength (λ) – distance from one point on the wave to the same point on the next wave; measured in metres (m).
Frequency (f) – number of waves passing a point per second; measured in hertz (Hz).
Crest (peak) – highest point above undisturbed position; trough – lowest point below.
Wavefront – a line representing a single wave; arrow (ray) shows direction of travel.
Wave speed – distance travelled by a wave each second.

Amplitude and wavelength

The Wave Equation

Wave speed equation: v = f × λ (v = wave speed in m/s, f = frequency in Hz, λ = wavelength in m).
Period (T) – time for one complete oscillation; T = 1/f (seconds).
Frequency and period are related: f = 1/T and T = 1/f.
Both transverse and longitudinal waves obey the wave equation.

Ripple tank patterns for low- and high-frequency vibration: higher frequency gives a shorter wavelength.

Transverse Waves

Transverse waves: vibration is perpendicular to direction of energy transfer.
Have peaks and troughs.
Examples: electromagnetic waves (light, radio, X-rays), ripples on water, seismic S-waves.
Mechanical transverse waves can travel in solids and on liquid surfaces, but not in liquids or gases.
Non-mechanical transverse waves (e.g., light) can travel in a vacuum.

Longitudinal Waves

Longitudinal waves: vibration is parallel to direction of energy transfer.
Have compressions (particles close together) and rarefactions (particles spaced apart).
Examples: sound waves, seismic P-waves.
Can travel in solids, liquids, and gases; cannot travel in a vacuum.
Density and pressure change along the wave.

Wave Behaviour: Reflection, Refraction, Diffraction

All waves can undergo reflection, refraction, and diffraction.
Reflection – wave hits a boundary and stays in the original medium; angle of incidence = angle of reflection.
Refraction – wave changes speed when entering a different medium; wavelength changes but frequency stays the same; direction may change (towards normal if slowing down, away if speeding up).
Diffraction – waves spread out when passing through a narrow gap or around an edge.
Diffraction is most prominent when gap width ≈ wavelength; larger gap → less diffraction.
Longer wavelengths diffract more than shorter wavelengths.

Ripple Tank Experiments

A ripple tank demonstrates wave properties using water waves.
Reflection: wavefronts reflect off a metal bar placed in the water.
Refraction: a glass block creates shallow water; waves slow down and wavelength decreases.
Diffraction: barriers with gaps or edges show spreading of waves.
Changing motor frequency changes wavelength: higher frequency → shorter wavelength.

Think like a scientist

Use a wave simulation to vary frequency while holding wave speed constant.
Comparison: the wave frequency in hertz. Outcome: wavelength in metres.
Control: keep the wave speed constant. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Wave relationships help explain sound, light and communications.
Changing frequency does not always leave speed unchanged; the constant-speed model needs a specified medium and conditions.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

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1.Which of the following is the correct definition of a wave?
Easy
- AA transfer of energy without transfer of matter
- BA transfer of matter without transfer of energy
- CA transfer of both energy and matter
- DA transfer of neither energy nor matter
2.The source vibrates with twice the amplitude while its frequency and wave speed stay constant. What happens to the wavelength?
Easy
- AIt stays the same
- BIt doubles
- CIt halves
- DIt becomes zero
3.Which of the following is a transverse wave?
Easy
- ASound wave
- BSeismic P-wave
- CLight wave
- DLongitudinal wave in a slinky
4.A wave has a speed of 3.0 m/s and a wavelength of 0.5 m. What is its frequency?
Medium
- A1.5 Hz
- B6.0 Hz
- C0.17 Hz
- D3.5 Hz
5.The source frequency doubles while the wave speed stays constant. What happens to the distance between neighbouring compressions?
Easy
- AIt halves
- BIt doubles
- CIt remains unchanged
- DIt becomes four times larger
6.Which of the following changes occurs when a water wave passes from deep water into shallow water?
Medium
- AIts frequency increases
- BIts wavelength decreases
- CIts speed increases
- DIts amplitude remains constant
7.A wave has a time period of 0.25 s. What is its frequency?
Easy
- A0.25 Hz
- B4.0 Hz
- C2.5 Hz
- D0.4 Hz
8.Diffraction of waves is most pronounced when:
Easy
- AThe gap is much larger than the wavelength
- BThe gap is approximately equal to the wavelength
- CThe gap is much smaller than the wavelength
- DThe wavelength is zero

複習筆記

## Big idea: wave speed, frequency and wavelength - **Key concept: Relationships.** Wave speed equals frequency times wavelength. Waves transfer energy without a net transfer of the medium through the whole wave journey. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Wave relationships help explain sound, light and communications. ## Wave Basics & Energy Transfer - Waves transfer **energy** without transferring **matter**. - Objects floating on water bob up and down but do not move with the wave – evidence that matter is not transferred. - Waves are described as **oscillations** or **vibrations** about a fixed point. - Ripples cause water particles to oscillate up and down; sound waves cause air particles to vibrate back and forth. ## Features of a Wave - **Amplitude** – maximum displacement from undisturbed position; measured in metres (m). - **Wavelength** (λ) – distance from one point on the wave to the same point on the next wave; measured in metres (m). - **Frequency** (f) – number of waves passing a point per second; measured in hertz (Hz). - **Crest** (peak) – highest point above undisturbed position; **trough** – lowest point below. - **Wavefront** – a line representing a single wave; arrow (ray) shows direction of travel. - **Wave speed** – distance travelled by a wave each second. ## The Wave Equation - Wave speed equation: **v = f × λ** (v = wave speed in m/s, f = frequency in Hz, λ = wavelength in m). - **Period** (T) – time for one complete oscillation; T = 1/f (seconds). - Frequency and period are related: **f = 1/T** and **T = 1/f**. - Both transverse and longitudinal waves obey the wave equation. ## Transverse Waves - **Transverse waves**: vibration is **perpendicular** to direction of energy transfer. - Have **peaks** and **troughs**. - Examples: electromagnetic waves (light, radio, X-rays), ripples on water, seismic S-waves. - Mechanical transverse waves can travel in solids and on liquid surfaces, but not in liquids or gases. - Non-mechanical transverse waves (e.g., light) can travel in a vacuum. ## Longitudinal Waves - **Longitudinal waves**: vibration is **parallel** to direction of energy transfer. - Have **compressions** (particles close together) and **rarefactions** (particles spaced apart). - Examples: sound waves, seismic P-waves. - Can travel in solids, liquids, and gases; **cannot** travel in a vacuum. - Density and pressure change along the wave. ## Wave Behaviour: Reflection, Refraction, Diffraction - All waves can undergo **reflection**, **refraction**, and **diffraction**. - **Reflection** – wave hits a boundary and stays in the original medium; angle of incidence = angle of reflection. - **Refraction** – wave changes speed when entering a different medium; wavelength changes but frequency stays the same; direction may change (towards normal if slowing down, away if speeding up). - **Diffraction** – waves spread out when passing through a narrow gap or around an edge. - Diffraction is most prominent when gap width ≈ wavelength; larger gap → less diffraction. - Longer wavelengths diffract more than shorter wavelengths. ## Ripple Tank Experiments - A **ripple tank** demonstrates wave properties using water waves. - **Reflection**: wavefronts reflect off a metal bar placed in the water. - **Refraction**: a glass block creates shallow water; waves slow down and wavelength decreases. - **Diffraction**: barriers with gaps or edges show spreading of waves. - Changing motor frequency changes wavelength: higher frequency → shorter wavelength. ## Think like a scientist - Use a wave simulation to vary frequency while holding wave speed constant. - **Comparison:** the wave frequency in hertz. **Outcome:** wavelength in metres. - **Control:** keep the wave speed constant. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Wave relationships help explain sound, light and communications. - Changing frequency does not always leave speed unchanged; the constant-speed model needs a specified medium and conditions. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Wave Behaviour: Describe reflection, refraction, and diffraction of waves, including the effects of gap size and wavelength on diffraction.
Ripple Tank Experiments: A **ripple tank** demonstrates wave properties using water waves.
Wave Properties: Identify and define amplitude, wavelength, frequency, period, wave speed, crest, trough, and wavefront.
Transverse & Longitudinal Waves: Distinguish between transverse and longitudinal waves in terms of direction of vibration, structure, and ability to travel in different media.
Wave Equation: Use the wave equation v = fλ and the relationship f = 1/T to solve problems involving wave speed, frequency, wavelength, and period.
Designing scientific inquiries: Plan a fair comparison: Use a wave simulation to vary frequency while holding wave speed constant.
Evaluating evidence and impacts: Wave relationships help explain sound, light and communications. Changing frequency does not always leave speed unchanged; the constant-speed model needs a specified medium and conditions.
Wave Basics & Energy Transfer: Waves transfer **energy** without transferring **matter**.
Features of a Wave: **Amplitude** – maximum displacement from undisturbed position; measured in metres (m).
The Wave Equation: Wave speed equation: **v = f × λ** (v = wave speed in m/s, f = frequency in Hz, λ = wavelength in m).
Transverse Waves: **Transverse waves**: vibration is **perpendicular** to direction of energy transfer.
Longitudinal Waves: **Longitudinal waves**: vibration is **parallel** to direction of energy transfer.
Wave Behaviour: Reflection, Refraction, Diffraction: All waves can undergo **reflection**, **refraction**, and **diffraction**.
energy: Waves transfer **energy** without transferring **matter**.
matter: Waves transfer **energy** without transferring **matter**.
oscillations: Waves are described as **oscillations** or **vibrations** about a fixed point.

字卡

Which of the following is the correct definition of a wave?

A transfer of energy without transfer of matter Waves transfer energy without transferring matter. For example, water waves cause a floating object to bob up and down but not move horizontally.

The source vibrates with twice the amplitude while its frequency and wave speed stay constant. What happens to the wavelength?

It stays the same Wavelength = wave speed / frequency. Neither changes, so wavelength stays the same.

Which of the following is a transverse wave?

Light wave Light is an electromagnetic wave and is transverse. Sound and seismic P-waves are longitudinal.

A wave has a speed of 3.0 m/s and a wavelength of 0.5 m. What is its frequency?

6.0 Hz Using v = f λ, f = v / λ = 3.0 / 0.5 = 6.0 Hz.

The source frequency doubles while the wave speed stays constant. What happens to the distance between neighbouring compressions?

It halves The distance between neighbouring compressions is the wavelength. With constant speed, doubling frequency halves wavelength.

Which of the following changes occurs when a water wave passes from deep water into shallow water?

Its wavelength decreases When water waves enter shallow water they slow down, so wavelength decreases. Frequency remains the same.

A wave has a time period of 0.25 s. What is its frequency?

4.0 Hz Frequency f = 1/T = 1/0.25 = 4.0 Hz.

Diffraction of waves is most pronounced when:

The gap is approximately equal to the wavelength Diffraction is greatest when the gap size is similar to the wavelength. If the gap is much larger, diffraction is negligible.

Which of the following is the correct unit for frequency?

Hertz (Hz) Frequency is measured in hertz (Hz), which is equivalent to s⁻¹.

A student measures the distance between 10 successive wave crests as 1.8 m. What is the wavelength?

0.2 m The distance between 10 successive crests spans 9 wavelengths (gaps between crests). So wavelength = 1.8 / 9 = 0.2 m.

In a ripple tank, the paddle vibrates at 5 Hz. The wave speed is 0.2 m/s. What is the wavelength?

0.04 m Using v = f λ, λ = v / f = 0.2 / 5 = 0.04 m.

Which of the following statements about reflection of waves is correct?

The angle of incidence equals the angle of reflection The law of reflection states that the angle of incidence equals the angle of reflection. Wavelength and frequency remain unchanged.

A water wave travels from deep water into shallow water. Which row describes what happens to the wave speed, frequency, and wavelength?

speed decreases, frequency stays the same, wavelength decreases When a wave enters shallow water, its speed decreases. Frequency is determined by the source and does not change. Since v = fλ, a decrease in speed with constant frequency causes a decrease in wavelength.

In a ripple tank, a vibrating paddle produces waves. The frequency of the paddle is increased. What happens to the wavelength of the water waves?

it decreases In a ripple tank, wave speed is constant for a given depth. Since v = fλ, if frequency increases, wavelength must decrease.

A wave has a speed of 0.25 m/s and a time period of 2.0 s. What is the wavelength?

0.50 m First find frequency: f = 1/T = 1/2.0 = 0.5 Hz. Then use v = fλ, so λ = v/f = 0.25/0.5 = 0.50 m.

A water wave passes from deep water into shallow water. Which of the following wave properties remains unchanged?

frequency Frequency is determined by the source and does not change when a wave enters a different medium. Speed and wavelength change, and direction may change due to refraction.

How would you design the inquiry for wave speed, frequency and wavelength?

Use a wave simulation to vary frequency while holding wave speed constant. Compare the wave frequency in hertz; record wavelength in metres; keep the wave speed constant.

What limitation matters when applying wave speed, frequency and wavelength?

Changing frequency does not always leave speed unchanged; the constant-speed model needs a specified medium and conditions.

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