Physics: Vibration Motion

• Physics for the Third Grade of Industrial Secondary Education during 2023-2024, written in English.

Table of Contents

• Chapter 1: Waves
• Chapter 2: Heat
• Chapter 3: Dynamic Electricity
• Chapter 4: Magnetic Effect of Electric Current
• Chapter 5: Electromagnetic Induction

Chapter 1: Waves

Lesson 1: Vibration Motion

• Periodic motion regularly returns an object to a given position after a fixed time interval like vibrational or wave motion.
• Vibrational motion examples include a simple pendulum, tuning fork, vibrating stretched string, and a weight attached to a vibrating spring.
• Displacement measures the distance between a vibrating body's position at any instant and its rest position.
• Amplitude (A), measured in meters (m), is the maximum displacement from the original position.
• Complete vibration is the motion of a vibrating body through an interval between successive passes at the same point in the same phase.
• Periodic Time (T), measured in seconds (sec), is the time for a vibrating body to complete one full vibration.
• Frequency (ν), measured in Hertz (Hz), specifies the number of complete vibrations (oscillations) per unit of time (one second).

Solved Example

• A simple pendulum makes 1200 vibrations per minute and covers 20 cm in each vibration.
• The amplitude: 0.05m
• Frequency = 20 Hz
• Periodic time = 0.05 sec

Lesson 2: Wave Motion

• Waves on water surfaces can push fishing floats or boats.
• Dropping a pebble creates a disturbance, generating waves spreading as concentric circles.
• Visible light and sound are common examples of waves in daily life
• Wave examples include waves on liquid surfaces, sound waves, waves on strings, and electromagnetic radiations like light, X-rays, radio waves, infrared, and ultraviolet radiation.
• A Wave is a disturbance that propagates and transports energy
• Waves propagate through a medium or space.

Types of Waves

• Mechanical waves propagate through a medium like sound or water
• Electromagnetic waves propagate through a medium or space, examples include light, x-rays
• Mechanical waves require a medium to propagate
• Electromagnetic waves do not require a medium to propagate

Conditions for Producing Mechanical Waves:

• A disturbance source (vibrator/oscillator)
• A medium to transmit the disturbance
• The transmission of disturbance from the source to the medium

Types of Mechanical Waves

• Longitudinal waves: particles vibrate in the same direction as wave propagation.
• The longitudinal wave propagates through compressions and rarefactions.
• Sound waves and waves on stretched strings are examples of longitudinal waves.
• Transverse waves: particles vibrate perpendicular to the wave's propagation direction.
• Transverse waves propagate through crests and troughs.
• Water waves and waves on a stretched wire are examples of transverse waves.

Wave Characteristics

• Wavelength (λ) is the distance between two successive points in phase, or the distance a vibrating body covers in one complete wave.
• λ = total distance / number of waves
• Frequency (ν) is the number of waves passing a point per second.
• ν= number of waves / total time
• Periodic time (T) is the time it takes for a wave to complete one full cycle.
• T = total time / number of waves
• Frequency and periodic time are inversely related and the equation is: ν = 1 / T

Wave Velocity, Frequency, and Wavelength Relationship

• Wave velocity (v) is the product of wavelength (λ) and frequency (ν): v = λν
• v is measured in meters per second (m/s).
• λ is measured in meters (m).
• ν is measured in Hertz (Hz).

Solved Example

• A sound wave with a 0.5m wavelength is produced by an audio source with a frequency of 666 Hz.
• Calculate the velocity of propagation of sound in air: which is 333m/s

Second Solved Example

• Given a diagram, find the amplitude, which is 6 cm
• Given a diagram, find the frequency which is 25 Hz
• Given a diagram, find the wavelength, which is 10 cm
• Given a diagram, find the velocity, which is 2.5 m/s

Lesson 3: Light

• Light is an electromagnetic wave occupying a small range within the electromagnetic spectrum, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and γ-rays.
• The sun's energy is divided almost equally between heat and light
• Plants use light from the sun for photosynthesis to produce their own food.
• Sound and light both demonstrate wave nature, but light doesn't need a medium to travel.
• Light is subject to reflection, refraction, interference, and diffraction.
• Electromagnetic waves, including light, travel at a constant speed of 3 × 10^8 m/s but vary in frequency.

Reflection and Refraction of Light

• Light travels in straight lines unless it meets an obstruction, which results in reflection, refraction, or partial absorption based on the medium's properties.

First: Reflection of light

• Reflection is the bouncing back of light into the same medium when it strikes a reflective surface like a mirror.
• Laws of Reflection
  • The angle of incidence equals the angle of reflection.
  • The incident ray, reflected ray, and normal lie in one plane perpendicular to the reflecting surface.

Caution

• Light striking a reflective surface perpendicularly reflects back on itself.
• In perpendicular reflection, the angle of incidence is zero and the angle of reflection is zero.

Two mirrors make an angle of 120° with each other

• A ray comes in on mirror M1 at 60° to the normal.
• Need to find the angle the ray makes with M2 after reflection from both mirrors

Secondly: Refraction of light

• Refraction is the bending of light as it passes from one medium to another, due to changes in speed caused by differing densities.

Two Laws of Refraction:

• The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, known as the refractive index (n12).
• n12 = v1/v2 = sin θ1 / sin θ2
• v1 speed of light in the first medium
• v2 speed of light in the second medium
• θ1: angle of incidence in the first medium
• θ2: angle of refraction in the second medium

The incident ray, refracted ray, and the normal lie in the same plane

• Absolute Refractive Index (n): Ratio of light speed in free space (air) (c = 3 × 10^8 m/s) to light speed in a medium.
• n = c / v = sin θ air / sin θ medium. Relative Refractive Index: Ratio of the absolute refraction index of the second medium to the first.
• n12 = n2 / n1 = v1 / v2 = sin θ1 / sin θ2.

Snell's Law

• Formula is n1 × sin θ1 = n2 × sin θ2.

Caution when using refractive index

• The definition of the absolute refractive index shows that the index of refraction is a dimensionless number greater than unity because v is always less than c.
• The relative refractive index may be more or less than one.
• When light travels from a denser to a less dense medium, the relative refractive index is less than one, and vice versa.

Exercise:

From the table of Mediums and Refraction index what happens to the speed of light when it travels:

• From air to glass?
• From water to glass?
• From glass to water?
• How to calculate the relative refractive index from glass to water?

Lesson 4: Total Internal Reflection

• The critical angle is the incidence angle in a denser medium (1st medium) corresponding to a 90° refraction angle in the less dense medium (2nd medium).
• Calculating the critical angle value: n1 × sin θ1 = n2 × sin θ2 and θ1 = θc (critical angle) if θ2 = 90°.
• Thus, the formula is written as, n1 × sin θc = n2 × sin 90°.

Solved Problem

• If glass and water have absolute refractive indexes of 1.6 and 1.33, calculate the critical angle for light moving from glass to water. Using the formula from above:
• 1.6 × sin θc = 1.33 × sin 90°
• θc = 56.23°.

Total Internal Reflection

• If light strikes the denser medium at an angle (θ) greater than the critical angle (θc), total internal reflection occurs, and all light is reflected internally without energy loss.

Applications of Total Internal Reflection

• Optical Fibers
• Fine, hollow tubes made of transparent material (glass or plastic) with a high refractive index (small critical angle).
• Light entering the tube undergoes successive reflections and emerges from the other end with minimal energy loss.
• Optical fibers transport light.
• Used in medical endoscopes and computer communications.
• Each fiber coated with a thin layer of a material of lower refractive index in order to keep the light rays inside the core without escaping or decreasing without loss of intensity.

Totally Reflecting Prism

• Composed of a 90° isosceles glass prism (90°, 45°, 45°).
• Total internal reflection occurs because the critical angle is approximately 42°.
• Changes the path of light rays by 90° or 180°.
• Used in optical equipment like periscopes and binoculars.
• It is more effective than metallic mirrors, and the reflection results in 100% accuracy. The metallic mirror reduces luster, decreasing reflection.
• The reflecting face of the prism is coated with a thin layer of aluminum fluoride or magnesium.

Chapter 2: Heat

• Lesson 1: Measuring Heat
• Lesson 2: Heat Transfer
• Understand the difference between temperature and heat.
• Measure temperature using different scales.
• List how energy changes as thermal energy transfers.
• Explain how liquid and thermometers correlate with temperature.
• Compare/Contrast the heat capacities and specific heat.

Lesson 1: Measuring Heat

• Temperature vs Heat
  • In everyday language, temperature and heat are interchangeable. But in physics, they have very different meanings.
  • Define temperature by how it's measured, then see how those changes affect object dimensions.
  • See that heat refers to energy transfer caused by temperature differences.
  • The concept of temperature is rooted in “hot” and “cold” based on our touch. A body that feels hot usually has a higher temperature than a similar body that feels cold.
  • Temperature- depends on the physical state of a material and is a quantitative description of its hotness or coldness.
  • Heat- refers to energy in transit from one body or system to another because of a temperature difference.
  • Many properties of matter that we measure depend on changing temperatures, such as the length of a metal rod or color of a hot glowing object.
  • At higher temperatures, the material changes from solid to liquid. Liquid to vapor state.
  • When matter is heated (gains temperature), its molecules go faster and take up more spaces. So, the solid, liquid, or gas expands, and vice versa. Rising temperatures make the liquid expand in the tube thermometer.

Thermometers and the Temperature Scales

• Devices used to measure objects/system temperatures
• Thermometers are based on the principle that some physical property of a system changes as the system's temperature changes.

Thermal Equilibrium

• It's the state in which two bodies in physical contact with each other have identical temperature.
• Thermal equilibrium measures temperature with thermometers.
• Place a thermometer in contact with an object and wait until the column of liquid in the thermometer.
• Then you can find the object's temperature because the thermometer is in thermal equilibrium.

Important details

• If two systems, A and B, are in thermal equilibrium, they have the same temperature.
• If two systems cannot be in thermal equilibrium, it means they have different temperatures.

Temperature Scales

• There are three scales to identify:
  • Celsius temperature scale (TC)
  • Fahrenheit temperature scale (TF)
  • Kelvin temperature scale (absolute temperature) (TK)

Converting Temperatures

• To change from Celsius to Kelvin use: TK = TC + 273
• To convert from Fahrenheit to Celsius, use: TF = (9/5 x TC) + 32

Basic Scales

• The freezing temp of pure water is OC, 32OF and 273K
• The boiling temp of pure water is 1000C, 212OF and 373K

Quick exercises

• Problem: When it reaches 50OF, what is the temperature in degrees Celsius and in kelvins?
• Problem: Rank the following temperatures from highest to lowest: (a) 0oC (b) 0 oF; (c) 260 K; (d) 77K (e) -180 oC.

Application

• Temperature is to measure hotness or coldness.
• Systems must be constructed on scales.
• Figures show familiar systems that measure temperature.
• Figures show that the thermometer measures in everyday elements that are a liquid (Mercury or alcohol) inside a glass capillary tube.
• Based on the principle that's regular changes the length between the volume of liquids with temp.

Calculating the temperature related to the measurement the length of liquid column in the

thermometer

• t = 100 x (Lt-L0) / (L100-L0) = 100 (Vt- V0) / (V100 - V0)
• Lt (Vt): length (temperature) of liquid column at temperature (t)
• Lo (Vo): length (temperature) of liquid column