General Properties Of Waves

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Notes

Wave Motion & Energy Transfer

Waves transfer **energy** without transferring **matter**.
Objects floating on water bob up and down but do not travel with the wave, showing no net movement of matter.
Waves are described as **oscillations** or **vibrations** about a fixed point.
Wave motion can be demonstrated using vibrations in ropes, springs, or water waves in a ripple tank.

Features of Waves

**Wavelength** (λ): distance from one point on a wave to the same point on the next wave (e.g., crest to crest). Measured in metres (m).
**Frequency** (f): number of waves passing a point per second. Measured in hertz (Hz).
**Amplitude** (A): maximum displacement from the undisturbed position to a peak or trough. Measured in metres (m).
**Crest** (peak): highest point above the equilibrium; **trough**: lowest point below equilibrium.
**Wave speed** (v): distance travelled by a wave each second. Measured in m/s.
**Wavefronts** represent waves from above; spacing between wavefronts indicates wavelength.

The Wave Equation

Wave speed equation: **v $= f \times$ λ** $(v =$ wave speed in $\frac{m}{s}, f =$ frequency in Hz, λ = wavelength in m).
Both transverse and longitudinal waves obey the wave equation.
Frequency and time period (T) are related: **f = 1/T**.
Example: A wave with speed 0.15 m/s and period 2 s has frequency 0.5 Hz and wavelength 0.30 m.

Transverse Waves

**Transverse waves**: vibrations are **perpendicular** to the direction of energy transfer.
They have **peaks** and **troughs**.
Can travel through solids and on liquid surfaces, but not through liquids or gases (except electromagnetic waves in vacuum).
Examples: electromagnetic waves (light, radio), water ripples, seismic S-waves.

Longitudinal Waves

**Longitudinal waves**: vibrations are **parallel** to the direction of energy transfer.
They consist of **compressions** (particles close together) and **rarefactions** (particles spread apart).
Can travel through solids, liquids, and gases, but not through a vacuum.
Examples: sound waves, seismic P-waves.

Reflection & Refraction

**Reflection**: a wave hits a boundary and stays in the original medium; angle of incidence equals angle of reflection.
**Refraction**: a wave passes into a different medium, changing speed, wavelength, and direction (frequency remains constant).
Angles are measured from the **normal** (line perpendicular to the boundary).
When waves slow down (enter denser medium), they bend **towards** the normal; when they speed up, they bend **away** from the normal.

Diffraction

**Diffraction**: waves spread out when passing through a narrow gap or around an obstacle.
The effect is most pronounced when the gap width is approximately equal to the wavelength.
As gap size increases relative to wavelength, diffraction becomes less noticeable.
Diffraction does not change the wavelength of the wave.

Reflection of a wave at a plane surface: angle of incidence equals angle of reflection.

Refraction of a wave entering a denser medium: wave bends towards the normal.

Practice questions

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1.Which of the following correctly describes what waves transfer?
Easy
- AMatter
- BEnergy
- CBoth matter and energy
- DNeither matter nor energy
2.State the term used to describe the distance from one point on a wave to the same point on the next wave.
Easy
3.A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the wave speed in m/s.
Easy
- A12
- B9
- C11
- D10
4.In a transverse wave, the direction of vibration is parallel to the direction of energy transfer.
Easy
True or false?
5.Complete the sentence about longitudinal waves.
Medium
In a longitudinal wave, the regions where particles are close together are called $____ and$ the regions where particles are spread apart are called ____.
6.A wave travels from air into glass. Which of the following changes occurs?
Medium
- AIts frequency increases
- BIts wavelength decreases
- CIts speed increases
- DIts direction remains unchanged
7.The time period of a wave is 0.02 s. Calculate its frequency in Hz.
Medium
- A50
- B55
- C45
- D60
8.Name the wave effect that occurs when a wave passes through a narrow gap and spreads out.
Medium

Slides

Waves Transfer Energy, Not Matter

Waves transfer energy from one place to another without transferring matter.
For example, sound waves travel through air, but the air molecules themselves do not travel with the wave.
A toy duck on water bobs up and down as waves pass, but it does not move horizontally – proving only energy moves.

A toy duck floats on water as waves pass. Which statement is correct?

The duck moves with the wave, showing matter is transferred.
The duck bobs up and down but stays in place, showing energy is transferred without matter.
The duck moves sideways because water particles travel with the wave.
The duck does not move at all because waves do not affect objects.

Wave Features

Key terms: crest (peak), trough, amplitude, wavelength, frequency, wave speed.
Amplitude is the maximum displacement from the undisturbed position (measured in metres).
Wavelength (λ) is the distance between two consecutive identical points on a wave (e.g., crest to crest).
Frequency (f) is the number of waves passing a point per second (unit: hertz, Hz).

$The ____ of a$ wave is the distance from the undisturbed position to a crest or trough.

The Wave Equation

Wave speed $(v) =$ frequency $(f) \times$ wavelength (λ).
v is measured in m/s, f in Hz, λ in m.
This equation applies to all waves – transverse and longitudinal.

A wave has frequency 2 Hz and wavelength 0.5 m. What is its speed?

0.25 m/s
1.0 m/s
2.5 m/s
4.0 m/s

Transverse Waves

In transverse waves, vibrations are perpendicular to the direction of energy transfer.
Examples: electromagnetic waves (light, radio), water ripples, seismic S-waves.
They can travel in solids and on liquid surfaces, but not in liquids or gases (except EM waves).

Which of these are transverse waves?

Sound waves
Light waves
Water ripples
Seismic P-waves

Longitudinal Waves

In longitudinal waves, vibrations are parallel to the direction of energy transfer.
They consist of compressions (particles close together) and rarefactions (particles spread apart).
Examples: sound waves, seismic P-waves.
They can travel through solids, liquids, and gases, but not through a vacuum.

Which statement about longitudinal waves is correct?

Vibrations are perpendicular to the wave direction.
They have crests and troughs.
They cannot travel through a vacuum.
They only travel through solids.

Reflection and Refraction

Reflection: a wave hits a boundary and bounces back into the original medium. The angle of incidence equals the angle of reflection.
Refraction: a wave changes speed and direction when passing from one medium to another. Wavelength changes, but frequency stays the same.
The normal is an imaginary line perpendicular to the boundary.

When a wave refracts, $its ____$ changes but $its ____$ stays the same.

Diffraction

Diffraction is the spreading out of waves when they pass through a narrow gap or around an obstacle.
The effect is most noticeable when the gap width is similar to the wavelength.
If the gap is much larger than the wavelength, diffraction is negligible.

When does diffraction of waves through a gap become most prominent?

When the gap is much larger than the wavelength
When the gap is much smaller than the wavelength
When the gap is approximately equal to the wavelength
Diffraction does not depend on gap size

Comparing Transverse and Longitudinal Waves

Transverse: vibration perpendicular to wave direction; have crests and troughs; can travel in solids and on liquid surfaces; EM waves can travel in vacuum.
Longitudinal: vibration parallel to wave direction; have compressions and rarefactions; can travel in solids, liquids, and gases; cannot travel in vacuum.

Which properties apply to longitudinal waves?

They have compressions and rarefactions.
They can travel through a vacuum.
Vibrations are parallel to the wave direction.
Examples include light and water ripples.

Summary: Wave Behaviour

All waves can be reflected, refracted, and diffracted.
Reflection: angle of incidence = angle of reflection.
Refraction: change in speed causes change in direction and wavelength; frequency constant.
Diffraction: spreading occurs when gap is similar to wavelength.

Which wave property remains unchanged during refraction?

Speed
Wavelength
Frequency
Direction

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