Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define a pulse and a transverse wave.
• Identify key characteristics: amplitude, wavelength, frequency, period, crest, and trough.
• Draw and label a transverse wave.
• Use the wave equation v = fλ to solve problems.

Lesson summary

Waves are everywhere! From the radio waves that bring us our favourite music to the seismic waves that shake the ground during an earthquake, understanding wave phenomena is crucial to understanding the world around us. This week, we'll be focusing on the basics: pulses and transverse waves. This knowledge is fundamental for understanding more complex wave phenomena later on, including light and sound. Understanding waves helps us understand how cellphone towers work, how music travels to our ears, and even how sonar helps fisherman find schools of fish in the ocean.

Lesson notes

2.1 Pulses: A pulse is a single disturbance that moves through a medium. Imagine flicking a rope once. The single "bump" that travels down the rope is a pulse. A pulse carries energy, but the medium itself (the rope) doesn't travel with the pulse; the particles of the rope simply move up and down (or side to side) briefly and then return to their original positions. 2.2 Transverse Waves: A transverse wave is a wave in which the particles of the medium vibrate perpendicularly (at right angles) to the direction the wave travels. Imagine shaking a rope up and down continuously. The wave you create is a transverse wave. Light is an example of a transverse wave, although it doesn't require a medium to travel.

Key Characteristics of Transverse Waves: Crest: The highest point on a transverse wave.

Trough: The lowest point on a transverse wave.

Amplitude (A): The maximum displacement of a particle from its resting position. It's the height of the crest (or the depth of the trough) measured from the resting position. The amplitude is related to the energy of the wave; a larger amplitude means more energy. Wavelength (λ - lambda): The distance between two successive crests (or two successive troughs) on a wave. It's a measure of the length of one complete wave cycle.

Frequency (f): The number of complete wave cycles that pass a given point per second. It is measured in Hertz (Hz), where 1 Hz = 1 wave cycle per second.

Period (T): The time it takes for one complete wave cycle to pass a given point.

It's the inverse of frequency: T = 1/f. It's measured in seconds (s).

Speed (v): The distance the wave travels per unit of time. It is measured in meters per second (m/s). 2.3 The Wave Equation: The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the wave equation: v = fλ This equation tells us that: If the frequency increases and the speed remains constant, the wavelength decreases. If the wavelength increases and the speed remains constant, the frequency decreases. If the speed increases and the frequency remains constant, the wavelength increases. 2.4 Example Problems: Example 1: A transverse wave on a string has a frequency of 5 Hz and a wavelength of 2 meters. What is the speed of the wave?

Given: f = 5 Hz, λ = 2 m Required: v Equation: v = fλ Solution: v = (5 Hz)(2 m) = 10 m/s Therefore, the speed of the wave is 10 m/s.

Example 2: A wave travels at a speed of 20 m/s and has a wavelength of 4 meters. What is the frequency of the wave?

Given: v = 20 m/s, λ = 4 m Required: f Equation: v = fλ => f = v/λ Solution: f = (20 m/s) / (4 m) = 5 Hz Therefore, the frequency of the wave is 5 Hz.

Example 3: A group of learners create a transverse wave in a long spring. They observe that 10 complete waves pass a point in 2 seconds. If the wavelength of the wave is 0.5 meters, what is the speed of the wave?

Given: 10 waves in 2 seconds, λ = 0.5 m Required: v First, calculate the frequency: f = (number of waves) / (time) = 10 waves / 2 s = 5 Hz Equation: v = fλ Solution: v = (5 Hz)(0.5 m) = 2.5 m/s Therefore, the speed of the wave is 2.5 m/s. Guided Practice (With Solutions)

Question 1: A pulse is sent down a rope. Describe what happens to the rope particles as the pulse passes.

Solution: The rope particles move perpendicularly (up and down, or side to side) to the direction of the pulse. They are momentarily displaced from their resting positions, but they return to their original positions after the pulse has passed. The rope particles do not travel along with the pulse.

Question 2: A transverse wave has a crest that is 0.2 meters above the resting position. What is the amplitude of the wave?

Solution: The amplitude is the maximum displacement from the resting position, which is the height of the crest.

Therefore, the amplitude is 0.2 meters.

Question 3: A transverse wave has a wavelength of 3 meters and a frequency of 4 Hz. Calculate the speed of the wave.

Solution: Given: λ = 3 m, f = 4 Hz Required: v Equation: v = fλ Solution: v = (4 Hz)(3 m) = 12 m/s The speed of the wave is 12 m/s.

Question 4: The speed of a wave is 15 m/s, and its frequency is 3 Hz. What is the wavelength of the wave?

Solution: Given: v = 15 m/s, f = 3 Hz Required: λ Equation: v = fλ => λ = v/f Solution: λ = (15 m/s) / (3 Hz) = 5 m The wavelength of the wave is 5 meters. Independent Practice (Questions Only) What is the difference between a pulse and a continuous transverse wave? Draw a diagram of a transverse wave and label the crest, trough, wavelength, and amplitude. A transverse wave has a wavelength of 0.8 meters and a frequency of 10 Hz. Calculate the speed of the wave. A wave travels at a speed of 30 m/s and has a frequency of 6 Hz. What is the wavelength of the wave? The period of a transverse wave is 0.2 seconds. What is its frequency? A group of Grade 10 learners create a wave in a rope, and observe that 5 crests pass a specific point in 1 second.