DP IB Physics: SL

C. Wave behavior

C.2 Wave model

DP IB Physics: SL C. Wave behavior C.2 Wave model Guiding questions:
a)	What are the similarities and differences between different types of waves?
b)	How can the wave model describe the transmission of energy as a result of local disturbances in a medium?
c)	What effect does a change in the frequency of oscillation or medium through which the wave is travelling have on the wavelength of a travelling wave?

DP IB Physics: SL

C. Wave behavior

C.2 Wave model

Guiding questions:

What are the similarities and differences between different types of waves?

How can the wave model describe the transmission of energy as a result of local disturbances in a medium?

What effect does a change in the frequency of oscillation or medium through which the wave is travelling have on the wavelength of a travelling wave?

a) What are the similarities and differences between different types of waves?
Solution:
Although they differ in their modes of propagation, waves—which transport energy without moving matter—share characteristics such as wavelength, frequency, and amplitude.
Whereas longitudinal waves, like sound, entail parallel motion, transverse waves, like light, involve particle motion perpendicular to energy transfer.
Additionally, they vary in whether they require a medium to move; electromagnetic waves do not require a medium, but mechanical waves must.
⇒ Similarities between different types of waves:
These traits are shared by all waves, whether they are electromagnetic or mechanical.

Feature	Explanation
Transfer energy	Waves carry energy from one point to another without transporting matter overall
Wavelength ( λ )	Distance between two corresponding points on a waves (e.g crest to crest)
Frequency ( f )	Number of wave cycles per second (measured in hertz, Hz)
Amplitude	Maximum displacement from rest – relates to energy carried by the wave
Wave speed (v)	[math]\text{Speed} = \text{frequency} \times \text{wavelength} \\ v = f \lambda[/math]
Reflection	Bouncing off surfaces
Refraction	Changing direction when entering a new medium
Diffraction	Spreading out when passing through opening or around obstacles
Interference	Superposition of waves can create constructive or destructive effects

Figure 1 Longitudinal and transverse waves
⇒ Differences between types of waves:

Feature	Mechanical Waves	Electromagnetic waves
Medium required	Need a material (solid, liquid, or gas)	No – can travel through
Wavelength ( λ )	Sound, Water waves, Seismic waves	Light, ratio waves, X – rays
Frequency ( f )	Properties of the medium	Medium (if any) and wave frequency
Amplitude	Can be both	Always transverse
Wave speed ( v )	Cannot travel through vacuum	Travel fastest in vacuum

b) How can the wave model describe the transmission of energy as a result of local disturbances in a medium?
Solution:
The wave model describes how particles oscillate and transfer energy to nearby particles in a medium when there is a local disturbance (such as an impact or vibration), enabling energy to flow through the medium without the bulk movement of matter.
Figure 2 Electromagnetic waves
⇒ Understanding the wave model:
A wave is a recurring disruption that transports energy from one location to another via a medium (or space).
When energy is applied to a spot in a medium in the wave model:
– Particles are moved out of their places of equilibrium.
– These particles engage in interactions with nearby particles.
– A wave is produced when the disturbance is transmitted as an oscillation.
⇒ Transmission Mechanism in the wave model:
1. A force, sound, drop, etc., disturbs a particle.
2. It starts oscillating, or vibrating back and forth.
3. This movement applies a force of restoration to nearby particles.
4. Adjacent particles start to vibrate—the wave moves
5. Even if particles just vibrate, energy is transferred across the medium.
c) What effect does a change in the frequency of oscillation or medium through which the wave is travelling have on the wavelength of a travelling wave?
Solution:
A wave’s wavelength is determined by its frequency as well as its speed, both of which are influenced by the medium.
The wave equation states that variations in the frequency or the medium will have an impact on the wavelength:
[math]v = f \lambda[/math]
Figure 3 Transverse wave
A wave’s wavelength will vary if its oscillation frequency or the medium it passes through changes.
Assuming the wave’s speed is constant, the wavelength reduces as the oscillation frequency rises and vice versa.
Although a wave’s wavelength and speed might alter when it moves through different materials, its frequency typically stays constant.
⇒ Changing frequency (same medium):
The speed v remains constant if the wave remains in the same medium.
[math]\lambda = \frac{v}{f}[/math]
– Light passing from air to glass:
Reduced speed results in a shorter wavelength, which causes light to bend towards the normal (refraction).
– Sound from air into
Increases in speed lead to increases in wavelength.
⇒ Effect of medium:
A wave’s speed can alter as it moves through different media. For instance, sound waves move through solids, water, and air at varying rates.
The wavelength must alter to account for the change in speed if the frequency stays constant, which frequently happens as a wave moves between mediums.
The wave’s wavelength grows when it accelerates up and reduces when it slows down.