Lesson 7.3: Wave Properties and Behaviour

Introduction

Welcome to Lesson 7.3 of Foundation Physics, students! Today, we will explore the fascinating world of waves and their properties. 🎢 By the end of this lesson, you will be able to:

• Understand the difference between transverse and longitudinal waves.
• Describe key characteristics of waves: amplitude, wavelength, frequency, period, and wave speed! 🌊
• Learn about phase and phase difference through graphs.
• Understand the concepts of polarisation, reflection, refraction, and total internal reflection in waves.
• Relate the properties of a wave effectively using the equation $c = f\lambda$.

Let’s dive into the world of oscillations, waves, and optics!

Transverse and Longitudinal Waves

Waves are fascinating phenomena that transfer energy from one place to another without transferring matter. There are two primary types of waves: transverse waves and longitudinal waves.

Transverse Waves

In transverse waves, the motion of the medium is perpendicular to the direction of wave travel. A common example is a wave on a string or water waves. 🌊 In a transverse wave, you can identify the following properties:

• Amplitude (A): The maximum displacement of points on a wave from their rest position. The height of the wave crest!
• Wavelength (λ): The distance between two consecutive crests or troughs (the peak and lowest points of the waves).
• Frequency (f): The number of waves that pass a point in one second.
• Period (T): The time it takes for one complete wave cycle to pass a point.
• Wave Speed (c): The speed at which the wave travels through the medium, given by the formula

$$

$ c = f \lambda$

$$

Longitudinal Waves

In longitudinal waves, the displacement of the medium is parallel to the direction of wave propagation. This means the particles in the medium move back and forth along the direction of the wave. A great example of a longitudinal wave is sound! 🎶

• Compressions: Regions where particles are close together,
• Rarefactions: Regions where particles are spread apart.

Comparing Types of Waves

| Property | Transverse Waves | Longitudinal Waves |

|---------------------|--------------------------|----------------------------|

| Direction of Motion | Perpendicular | Parallel |

| Example | Light waves, waves on strings | Sound waves |

Phase and Phase Difference

When discussing waves, understanding the concept of phase is crucial. The phase of a wave refers to a specific point in the wave cycle, and phase difference tells us how far apart two waves are in this cycle.

• The phase can be represented in degrees or radians. A complete cycle corresponds to $360°$ or $2π$ radians.
• If two waves are in phase, they have a phase difference of $0°$ or $360°$ (they reach their maximum displacement together).
• If they are out of phase, say by $180°$, they will cancel each other out and create destructive interference.

Graphically, you can represent wave displacement over time or distance. For instance:

• Displacement-Time Graph shows how the displacement of a wave changes with time at a given point.
• Displacement-Distance Graph shows how the displacement of a wave changes as you move through space.

Polarisation of Transverse Waves

Polarisation is a unique property of transverse waves. It occurs when waves vibrate in a single plane. For example, light waves can be polarised, helping reduce glare from surfaces like water or reflective roads. 🕶️

Real-World Example: Polarising Filters

Polarising filters, like those found in sunglasses, only allow light waves that vibrate in a certain direction to pass through, reducing the intensity of the light and glare.

Reflection and Refraction

Reflection

When waves hit a barrier, they bounce back. This is known as reflection. The law of reflection states that the angle of incidence equals the angle of reflection:

$$

$ \theta_i = \theta_r$

$$

Refraction

Refraction occurs when a wave passes from one medium to another, changing speed and direction. The relationship between the angles of incidence and refraction can be described by Snell's Law:

$$

$ n_1 \sin(\theta_1) = n_2 \sin(\theta_2}$

$$

where $n_1$ and $n_2$ are the refractive indices of the respective media, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction.

Total Internal Reflection

When light travels from a denser medium to a less dense medium, it can undergo total internal reflection if the angle of incidence exceeds a specific value known as the critical angle. This is what makes optical fibres work! 💡

Conclusion

This lesson explored the properties and behaviours of waves, including the differences between transverse and longitudinal waves, the concepts of phase and polarisation, as well as reflection and refraction. Remember that the speed of any wave can be calculated using the relationship $c = f\lambda$, which helps us understand how energy moves through different mediums. Through these concepts, you will gain a better appreciation of the role waves play in our everyday life! 🌍

Study Notes

• Types of Waves: Transverse (e.g., light, water) vs. Longitudinal (e.g., sound).
• Wave Properties:
• Amplitude (A)
• Wavelength (λ)
• Frequency (f)
• Period (T)

$ - Wave Speed (c = fλ)$

• Phase: Specific point in a wave cycle.
• Polarisation: Vibration in a single plane.
• Reflection: Angle of incidence = Angle of reflection.
• Refraction: Snell’s Law connects incidence and refraction angles.
• Total Internal Reflection: Occurs beyond the critical angle in optical fibres.