Lesson Notes By Weeks and Term v4 - SHS 2
WAVES
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WAVES
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 17
Grade code: 2.2.2.LI.4
Strand code: 2
Sub-strand code: 2
Content standard code: 2.2.2.CS.1
Indicator code: 2.2.2.LI.4
Theme: ENERGY
Subtheme: WAVES
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This lesson introduces the mathematical description of a progressive (or travelling) wave. Waves are all around us, from the sea waves at Busua beach to the radio waves that bring us broadcasts from Peace FM, and even the light waves from the sun. By understanding the wave equation, we can create a powerful mathematical model to predict a wave's behaviour at any point in space and time. This skill is fundamental to fields like telecommunications, medicine (ultrasound), and seismology.
Starter Activity (5 minutes) As a class, let's quickly review the basic properties of a wave using a Slinky spring. Amplitude (A): The maximum displacement from the equilibrium position. (Unit: meters, m) Wavelength (λ): The distance between two consecutive points in the same phase (e.g., crest to crest). (Unit: meters, m) Frequency (f): The number of complete oscillations per second. (Unit: Hertz, Hz) Period (T): The time taken for one complete oscillation. `T = 1/f`. (Unit: seconds, s) Wave Speed (v): The speed at which the wave energy propagates. `v = fλ`. (Unit: meters per second, m/s)
These five quantities are the building blocks we need to describe our wave mathematically. A. From Simple Harmonic Motion to a Travelling Wave
Imagine a single particle on a rope. If you shake the end of the rope up and down, that particle will oscillate in Simple Harmonic Motion (SHM). Its vertical displacement, `y`, at a time `t` can be described by: `y = A sin(ωt)`
Here, `A` is the amplitude, and `ω` is the angular frequency. Angular Frequency (ω): This tells us how quickly the particle oscillates in *time*. It's related to the regular frequency `f` and period `T`. > Formula: `ω = 2πf` or `ω = 2π / T` > Unit: radians per second (rad/s)