1.

Introduction to Properties of Waves

Key Concepts:

• Waves transfer energy from one point to another without transferring matter.
• Two main types of waves:
a. Transverse waves: Vibrations are perpendicular to the direction of travel of wave
(e.g., light, water waves).

b. Longitudinal waves: Vibrations are parallel to the direction of travel of wave (e.g.,
sound waves, seismic P-waves).
 • Key properties of waves:
a. Wavelength (λ): Distance between two consecutive crests or trough (meter,m)
b. Frequency (f): Number of wave cycles per second, measured in Hertz (Hz) or s-1.
c. Amplitude, (A): Maximum displacement from the rest position. (meter,m)
d. Time Period(T): the amount of time it takes for a complete wave to occur.
e. (seconds, s)
f. Wave speed (v): Speed at which a wave propagates (ms-1), given by:

v=fλ f =1/T

Example 1 : 3x108ms-1

Example 2: 1.25m
2. Sound

Sound is produced by vibrating sources. The vibrations travel through solids, liquids or gases.

Sound requires a medium to travel because they are carried by molecules.

Sound waves cause particles to vibrate parallel to the direction of wave travel.

The frequency range of human hearing is 20Hz (lower limit) to 20kHz (higher limit) or 20 Hz to
20 000Hz

When travelling through air, the speed of sound is approximately 330 m/s.

Sound cannot travel through a vacuum because there are no particles to carry the vibrations.

The speed of sound in air can be measured using distance and time.

Echo is the reflection of sound waves.

Ultrasound: Sound waves with a frequency higher than 20kHz.

Sound waves are longitudinal, consisting of compressions and rarefactions.

Sound travels fastest in solids, slower in liquids, and slowest in gases.

Longitudinal waves show areas of compression and rarefaction:

• Compressions are regions of high pressure due to particles being close together.
• Rarefactions are regions of low pressure due to particles being spread further apart.

a. Properties of sound
The frequency of a sound wave is related to the pitch that is heard:

• High frequency sound waves are high pitched. (girl’s voice)

• Low frequency sound waves are low pitched. (boy’s voice)

The amplitude of a sound wave is related to the volume of the sound:

• High amplitude sound waves are loud.

• Low amplitude sound waves are quiet.
 1. Quiet, low pitch sound.
2. Loud, low pitch sound.
3. Loud, high pitch sound.

Example Calculations:

Speed of Sound Calculation:

o A sound wave travels 340m in 2 seconds. Find the speed of sound.170ms-1

Echo Calculation:

a. A person hears an echo 0.5s after shouting near a wall 85m away. Find the
speed of sound.340ms-1

b. 0.24s
3. Seismic Waves

A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or
another planetary body. It can result from an earthquake, volcanic eruption, magma movement.
It can be artificially generated by human.

Seismic P-Waves (Primary Waves):

• Longitudinal waves that travel through solids and liquids.

• Fastest seismic waves, arriving first at seismic stations.
• Used to study Earth's interior structure.

Seismic S-Waves (Secondary Waves):

• Transverse waves that only travel through solids.

• Slower than P-waves but cause more ground movement.
• Cannot pass through Earth's liquid outer core, providing evidence for its structure.

P-Wave Travel Time Calculation:

A P-wave travels at 6000 m/s through Earth's crust. How long does it take to travel 30 km? 5s

S-Wave Travel Time Calculation:

An S-wave travels at 4000 m/s through Earth's mantle. How long does it take to travel 20 km? 5s
4. Other properties of waves (reflection, refraction)

a. Reflection of Waves (light of sound):

• When waves hit a plane surface, they bounce back.

• During reflection, speed, wavelength and frequency do not change
• Formula: Angle of incidence = angle of reflection
•

o Normal: A perpendicular line to the surface.

o Angle of Incidence: The angle between the incident ray and the normal.
o Angle of Reflection: The angle between the reflected ray and the normal.

Applications: Mirrors, sonar, and echolocation.

•
B. Plane Mirrors (Reflection of Light)

A plane mirror forms an image of an object, which is:

a. upright but laterally inverted i.e. the image is reversed left to right

b. the same size as the object

c. the same distance behind the mirror as the object is in front.
d. Virtual → the image cannot be formed on screen.

Plane mirrors are used in periscopes, security mirrors and dressing table mirrors.
Simple ray diagrams can be used to show how light reflects to form an image.

c. Refraction of Waves:

Refraction is the change in direction of light when it passes from one transparent medium to
another with different density. e.g from air to glass. When this happens their speed changes,
causing them to bend.

Water waves slow down in shallow water, bending towards the normal. Light bends when
passing through materials like glass or water.

Refraction ray diagram

The angle of incidence, i is angle between the incident ray and the normal.

The angle of refraction, r, is angle between the refracted ray and the normal.
From less dense to more dense (e.g air to glass), light bends towards the normal

From more dense to less dense (e.g. glass to air), light bends away from the normal

When passing along the normal (perpendicular) the light does not bend at all.

Refraction diagram of light from air through a glass block

The change in direction is due to the change in speed. When light passes into a denser
substance, the waves will slow down; so, they bend towards the normal. The speed and
wavelength changes but the frequency of waves does not change.

Light with the same colour will have the same frequency e.g. red has a low frequency, whilst blue
has a high frequency. When light refracts, it does not change colour.

D. Dispersion of light (using prism)

When white light passes through a prism, red light bends the least because it travels the fastest,
while violet light bends the most because it travels the slowest. That’s why red appears at one
end of the rainbow and violet at the other.
e. Thin converging lens

Principal Axis - A line that passes through the optical center of a lens.

Principal Focus (Focal Point) F - The point at which two rays traveling parallel to the principal
axis converge after passing through a converging lens.

Focal Length - The distance between the optical center of the lens and the principal focus.

Rays of light from an object at distance can be assumed to be parallel.

A ray passing through the centre of a lens is NOT refracted.

Ray parallel to the principal axis, after refraction, passes through the principal focus
point F.

Image is real, inverted and has the same size as object

5. Electromagnetic Spectrum

• The electromagnetic spectrum includes radio, microwave, infrared, visible, ultraviolet,

X-ray, and gamma rays, ordered by increasing frequency and decreasing wavelength.
• All electromagnetic waves travel at the same speed (3.0 × 10⁸ m/s) in a vacuum.
• Applications include:
o Radio waves: transmitting TV programmes or TV communication (radio, radar,
phones)
o Microwaves: spacecraft communication, satellite communication
o Infrared: Remote controls, thermal imaging, cooking
o Visible light: Vision(eyesight), photography
o Ultraviolet: Detecting fake banknotes (detecting forgery)
o X-rays: Medical imaging, security scanning (like airport baggage scanners)
o Gamma rays: sterilizing medical equipment, kills cells or tissues (cancer treatment)

Ultraviolet causes skin cancer, eye damage, premature aging therefore need to wear sunscreen
and sunglasses.

X-rays can damage DNA, therefore need to wear lead shield or apron during x-ray scan.
Gamma rays causes cell mutations, radiation sickness. Thick lead shield can provide protection
from gamma rays.

Example Calculations:

1. Wavelength of a Wave:
o A radio wave has a frequency of 100 MHz. Find its wavelength. 3x10 m 4

2. Frequency Calculation:
o An X-ray has a wavelength of 1 × 10⁻¹⁰ m. Find its frequency. 3x10 18
Hz

Example Calculation:

• If a person stands 2m away from a plane mirror, their image appears 2m behind the
mirror, making the total distance between them and their image 4m.

Questions-properties of waves
Questions-sound
Answers-properties of waves
Answers-sound