Physics Term 2-3 Formulas PDF

Physics Term 2-3 FORMULAS \\  1. WAVE PROPERTIES Objects that vibrate can transfer energy through waves. Waves are caused by some sort of disturbance in a specific medium followed by the propagation of energy Regardless of the type of wave observed, we can see a transfer of energy...

Physics Term 2-3 FORMULAS \\  1. WAVE PROPERTIES Objects that vibrate can transfer energy through waves. Waves are caused by some sort of disturbance in a specific medium followed by the propagation of energy Regardless of the type of wave observed, we can see a transfer of energy but not necessarily a transfer of matter Wave Mode -l A wave can be described as disturbance/oscillation/vibration that carries energy. Periodic waves repeat themselves at regular intervals. The transfer of energy is in the direction the wave is traveling, which is away from the source of vibration Features of a Wave Features of a Wave A wave can be visualized as a moving series of high points and low points. A crest is the high point of the wave. A trough is the low point. - The amplitude is the max. displacement on the wave from its rest position. It is NOT the same as the distance from crest to trough, which in water waves is the wave height or wave elevation. - Wavelength is the distance from any point on a wave to the same point on the next cycle of the wave, e.g.: the distance crest to crest. Assigned the symbol λ (Greek letter lambda) - Frequency, f, is the number of waves that pass a fixed point per second. Units: hertz (Hz) The period is the time it takes a single wave to pass a fixed point. T = 1 / f and f = 1 / T  - The speed or velocity a wave travels is how fast the energy spreads away. Velocity is the product of the wave’s frequency and its wavelength 2. WAVE CLASSIFICATION Propagation of waves - Waves are categorized according to how they propagate or transfer energy from place to place. - There are two major groups of waves: mechanical waves and electromagnetic waves. - Mechanical waves travel through a medium, the particles of which vibrate about a rest position E.g.: Sound and water Waves - Electromagnetic (EM) waves are self-propagating, featuring oscillating and perpendicular electric and magnetic fields. Transverse vs. Longitudinal Waves Mechanical waves are classified as either transverse or longitudinal according to the direction of vibration relative to the direction of energy flow through a material. Transverse wave: vibrations occur in a plane perpendicular to the direction of propagation. e.g.: water and EM waves Longitudinal wave: particles of the medium vibrate in the same direction as the direction of propagation of the wave. e.g.: sound wave Transverse wave The particles within the medium move transversely, or at 90° to, the direction of propagation of the wave itself. As energy, not the medium, is being transferred by the wave, the particles in the medium move transversely to the direction of the energy propagation Longitudinal waves - Longitudinal waves (e.g.: sound waves) are difficult to draw. - We represent sound waves as sine curves. A compression is represented as a crest, a rarefaction, a trough. Longitudinal wave The movement of the particles in the medium occurs parallel to that of the wave propagation. 3. REFLECTION AND REFRACTION OF WAVES Absorption (No reflection): The object appears dark REFLECTION AND SCATTERING Waves (incl. EM waves) can be reflected from smooth, flat, mirror-like surfaces or from irregular, bumpy surfaces. Light scattering (diffuse reflection) can be thought of as the deflection of a ray from a straight path which can occur when reflection occurs from a rough or uneven surface Reflection: Light-scattering: REFRACTION Refraction: Bending of light through a medium in which light travels at a different velocity (esp. glass or water) Refraction: THE RAY MODEL EM waves (eg light) in diagrams are straight lines with arrow heads representing the travel direction. These “rays” are like an infinitely thin beam of EM radiation. THE NORMAL (In Reflection & Refraction) The normal is the line that is perpendicular to the reflecting or refracting surface at the point where the ray hits it. Draw as a dashed and labeled line. The incident ray, the reflected ray and the normal at the point of incidence all lie in one plane. That means they can all be drawn as though they lie on one flat sheet of paper. LAW OF REFLECTION The angle between the incident ray and the normal is the angle of incidence 𝜃𝑖 or 𝑖. The angle between the reflected ray and the normal is the angle of reflection 𝜃𝑟 or 𝑟. Law of Reflection: 𝑖 = 𝑟 WAVEFRONTS In a wave diagram, sometimes we draw lines, called wave fronts, that represent the positions of different crests. At each point along a wave front, the wave is moving perpendicular to the wave front. Wavefronts are perpendicular to rays FURTHER REFRACTION Imagine an axle with two wheels rolling along a pavement onto grass. It rolls more slowly on the grass due to interaction of the wheels with the blades of grass. Rolled at an angle, it will be deflected from its straight-line course. The wheel that first meets the grass slows down first. The axle pivots, and the path bends toward the normal. When both wheels reach the grass, it continues in a straight line at reduced speed. The refraction of light, when it moves from one medium to another, is like an axle travelling from sidewalk to grass and changing direction. Light slows down in glass and water due to increased optical density of the medium Refraction: When a wave, traveling at an angle, changes its speed upon crossing a boundary between two media, it bends. WAVELENGTH AND REFRACTION When undergoing refraction, the frequency of the wave does not change. The frequency of light arriving at the boundary is the same as the frequency of light travelling on from the boundary. From the wave equation v = fλ, wavelength decreases when the velocity decreases. REFRACTION OF LIGHT When light rays enter a medium in which their speed decreases, as when passing from… Air into glass/water, the rays bend toward the normal. When light rays enter a medium in which their speed increases, such as from… Glass/water into air, the rays bend away from the normal. Examples: Due to the refraction of light: Swimming pools appear shallower, A pencil in a glass of water appears bent, The air above a hot stove seems to shimmer, Stars twinkle. 4. Wave Interference Interference and Superposition - Effects arise when two or more waves arrive at the same place at the same time. - Interference: Waves from separate sources can interfere, meaning they combine to reinforce and/or cancel each other. - Superposition Principle: The resultant wave is the sum of the individual waves. - Superposition: The addition of waves is called superposition. Constructive and Destructive Interference Constructive interference: Two waves combine and the sum of their amplitudes is greater than individual waves alone (troughs coincide with troughs and crests coincide with crests). Destructive Interference: When the sum of 2 waves is less than the individual waves’ amplitude. Complete destructive interference: A complete loss of amplitude in the resulting wave produced by their superposition. How to add waves: https://www.youtube.com/watch?v=lFuPAE9GYeM Standing Waves Most waves we have looked at so far are progressive or traveling waves e.g.: water waves. Standing waves: When incident and reflected waves interfere and the resultant wave appears to stand still.  - The positions at which constructive and destructive interference occur are evenly spaced along the string/pipe. - Nodes: undisturbed points - Antinodes: points where the medium is disturbed the most. 5. SOUND & WAVE INTERFERENCE Sound - a mechanical wave (needs a medium) - a longitudinal compression wave (particles vibrate in the direction of propagation) - represented in diagrams as a transverse wave so that its wave properties can be visualized and described - In sound, compressed air (compressions) surrounded by air that has been spread apart (rarefactions). - A wavelength is the distance between compressions. Speed of sound - Speed of sound in air is 340 m/s - Sound can travel within solids or liquids.  - Denser mediums generally have higher speeds of sound. Example: Sound travels in air at a speed of 330 m/s. Calculate the wavelength of a sound wave with a frequency of 256 Hz. - A: v = f.λ - λ = 330 / 256 = 1.29 m SOUND: VIBRATIONS IN A MEDIUM - The origin of a sound wave in any medium is always a vibration. - The higher the pitch of the sound, the faster the rate of vibration of the object. - A loud (high-volume) sound is said to have a large amplitude. The drum is a good example of a device acting as a source of vibrational energy, producing zones of high air pressure (compression) and zones of low air pressure (rarefaction) propagating away at 340m/s. Seeing Sound Waves - The cathode-ray oscilloscope (CRO) is a device that allows us to view sound waves on a screen. - The areas where the displacement of the wave is above the baseline represent zones of compression, and where the displacement of the wave is below the baseline represent zones of rarefaction. In reality, what happens is that the sound-wave energy is converted into an electrical signal at the microphone. Echo - An echo is sound reflecting from a surface and bouncing back at you. - There needs to be a time difference between the reflected sound and the original sound so that you can hear the echo. The size of that time difference is a minimum of 0.1 seconds. Example: If sound travels around 340 m/s in air, how far do you have to be from the surface reflecting the sound for you to hear the echo? Answer: Distance = velocity × time Total distance the sound travels (s) = 0.1 x 340 = 34m Distance from surface = ½ x 34 = 17m 6. BEATS AND DOPPLER EFFECT Beats When two sources of sound the same amplitude but slightly different frequencies are heard together, there will be a rhythmic change to the volume of the sound due to interference. As the waves drift in and out of phase, the resultant amplitude will reach close to zero before increasing again. In the diagram, the difference between the freq is 20Hz. Therefore, beats are heard every 20th of a second (0.05s). Lets try it with an f-generator on phones. Doppler Effect Doppler Effect is the result of a wave source relative to the wave medium. Approaching sound source will have an increased frequency/pitch Sound Intensity To observe light reflected from a concave and a conex mirror and lebel the pole, centre nd focus of the mirror a ray diagram