● WAVELENGTH MODULE https://physics.info/waves/#:~:text=To%20propagate%20%2C%20in%20the%20sense,which%20a%20wave%20can%20propagate. A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables oscillate periodically around an equilibrium (resting) value at a specific frequency. A traveling wave occurs when the entire waveform moves in one direction; a standing wave occurs when two superimposed periodic waves move in opposite directions. The amplitude of vibration in a standing wave features nulls at some points when the wave amplitude seems reduced or even zero. Wave A wave is a disturbance in a medium that transports energy without causing net particle movement. Elastic deformation, pressure variations, electric or magnetic intensity, electric potential, or temperature variations are all examples. ● ● ● ● Water waves (ripples of gravity waves, not sound through water) Light waves S-wave earthquake waves Stringed instruments Torsion wave A crest is the highest point of a transverse wave. It’s a trough at the bottom. 2. Longitudinal Wave: The movement of the particles in the medium in a longitudinal wave is in the same dimension as the wave’s movement direction. Examples of longitudinal waves: ● ● ● Sound waves P-type earthquake waves Compression wave Parts of longitudinal waves: 1. 2. Compression-The particles are close together in this case. Rarefaction-Where the particles are dispersed 3. Electromagnetic Waves: Figure 1. Pictorial representation of waves. Characteristics of Waves Waves include the following characteristics: ● ● ● The particles of the medium traversed by a wave vibrate only slightly about their mean positions, but they are not permanently displaced in the wave’s propagation direction. Along with or perpendicular to the wave’s line of travel, each succeeding particle of the medium performs a motion quite identical to its predecessors. During wave motion, only energy is transferred, but not a piece of the medium. These are waves that are produced and propagated without the use of a material medium, i.e., they can pass through vacuum and any other material medium. Examples of electromagnetic waves: ● ● ● ● visible light ultra-violet light radio waves microwaves Types of Waves The several forms of waves are listed here: 1. Transverse Waves: Figure 2. Electromagnetic waves. Waves in which the medium moves at an angle to the wave’s direction. Examples of transverse waves: 4. Mechanical waves: ● Only a material medium can produce or propagate mechanical waves. Newton’s equations of motion apply to these waves. Examples of mechanical waves: ● ● ● waves on water surface waves on strings sound waves Mechanical waves are of two types: 1. 2. Transverse wave motion- The particles of the medium vibrate at right angles to the wave’s propagation direction in transverse waves. Transverse waves include string waves, surface water waves, and electromagnetic waves. The disturbance that travels in electromagnetic waves (which include light waves) is caused by the oscillation of electric and magnetic fields at right angles to the wave’s travel direction. Longitudinal wave motion- Particles in the medium vibrate back and forth around their mean location along the energy propagation direction in these sorts of waves. They’re also known as pressure waves. Longitudinal mechanical waves are what sound waves are. Frequency – The number of waves passing a spot in a certain amount of time is referred to as the frequency of a wave. The hertz (Hz) unit of frequency measures one wave every second. The frequency’s reciprocal is the period, and vice versa. Period=1 / Frequency OR Frequency = 1 / Period ● Speed – The speed of an object refers to how quickly it moves and is usually stated as the distance traveled divided by the time it takes to travel. The distance traveled by a specific point on the wave (crest) in a given amount of time is referred to as the wave’s speed. A wave’s speed is thus measured in meters per second or m/s. Sample Problems 5. Matter waves: Problem 1: In a specific medium, a wave travels at 900 meters per second. Calculate the wavelength of a specific point in the medium if 3000 waves pass through it in 2 minutes. These waves are linked to the movement of matter particles. Solution: Examples of matter waves: The speed of a wave in medium v = 900 ms-1 ● ● ● electrons protons neutrons Formula for Speed of Wave It’s the entire distance a wave travels in a particular amount of time. The formula for calculating wave speed is as follows: Wave Speed = Distance Covered/Time taken Properties of Waves The following are the primary characteristics of waves: ● ● ● Amplitude – A wave is a form of energy transmission. The amplitude of a wave is its height, which is commonly measured in meters. It is proportional to the quantity of energy transported by a wave. Wavelength – A wavelength is a distance between identical locations in adjacent cycles of crests of a wave. In addition, it is measured in meters. Period – A wave’s period is the amount of time it takes a particle on a medium to complete one complete vibrational cycle. Because the period is a unit of time, it is measured in seconds or minutes. Freq. of wave = no. of waves passing per sec (n) = 3000 waves/2 min = 3000 / 2 × 60 = 25 s Wave length (λ) = ? v = n × (λ) λ = v/n = 900/25 = 36 m Problem 2: What distinguishes the roar of our national animal from that of a mosquito? Solution: The buzzing of a mosquito creates a sound of high pitch and low intensity or loudness, but the roaring of a national animal (tiger) produces a sound of low pitch and high intensity or loudness. Problem 3: Is it feasible to tell when a vessel maintained beneath the faucet is going to overflow? Solution: The length of an air column is inversely related to the frequency of the note it produces. The length of the air column above the vessel reduces as the level of water in the vessel rises. It generates a sound with a decreasing frequency, i.e. the sound gets shorter. It is possible to determine whether the vessel is filled with water based on the shrillness of the sound. Problem 4: The bottom of a ship in the sea shoots SONAR waves straight down into the saltwater. After 3.5 s, the signal reflects off the deep bottom bedrock and returns to the ship. When the ship reaches 100 km, it transmits another signal, which is received after 2 s. Calculate the depth of the sea in each example, as well as the height difference between the two. Solution: Velocity of SONAR waves in water C = 1500 ms-1 Time taken by be wave after reflection from the bottom of sea 2t = 3.5s REPORT 1: STANDING WAVES What is a standing waves? - Standing waves are formed by the superposition of two travelling waves of the same frequency (with the same polarisation and the same amplitude) travelling in opposite directions. - The animation depicts two waves moving through a medium in opposite directions. As is the case in any situation in which two waves meet while moving along the same medium, interference occurs. The two waves interfere to form a new wave pattern known as the resultant. The resultant in the animation below is shown in black. The resultant is merely the result of the two individual waves added together in accordance with the principle of superposition. - Standing waves are called standing waves because they look stationary, hence the word ‘standing’. What are nodes and antinodes? - Antinodes are points on a stationary wave that oscillate with maximum amplitude. Nodes are points of zero amplitude and appear to be fixed. - NODES for no displacement - ANTINODES for displacement (movement) t =1.75s Distance covered (d) = ? C = d/t => d = c.t = 1500 × 1.75 – 2625 m After moving 100km The time taken by the wave = 2t = 2s T = 2/2 = 1s d =? d = 1500 × l = 1500 The difference between these two heights = 2625 – 1500 = 1125m Problem 5: Why does a tone sound louder in an empty room than in a room with furniture and other objects? Solution: Sound is an energy form. The majority of the energy is absorbed by the furniture that acts as an obstruction. As a result, the strength of sound decreases, yet in an empty room, the intensity of sound remains relatively constant due to the absence of impediments, and we perceive it as louder. - Nodes are points of no displacement. Antinodes oscillate between large negative and positive displacement. How are standing waves formed? - Standing waves are produced whenever two waves of identical frequency interfere with one another while traveling opposite directions along the same medium. Examples (everyday formation of standing waves) - One easy example to understand standing waves is two people shaking either end of a jump rope. If they shake in sync the rope can form a regular pattern of waves oscillating up and down, with stationary points along the rope where the rope is almost still (nodes) and points where the arc of the rope is maximum (antinodes). - Acoustic guitar - The fixed strings of the guitar act as a medium - Whistling - Here, the air acts as a medium - Flute - The body of the flute acts as a contained medium REPORT 2: RESONANCE Definition - - A phenomenon in which an external force or a vibrating system forces another system around it to vibrate with greater amplitude at a specified frequency of operation. Resonance occurs when the matching vibrations of another object increase the amplitude of an object’s oscillations. Examples - Music instrument - Swing - Bridge Types of resonance 1. Mechanical resonance - Mechanical resonance occurs in physical systems with mass and elasticity, such as mechanical structures, musical instruments, or even bridges. When an external force is applied at the natural frequency of the system, it can cause the system to vibrate with increasing amplitude, which can lead to mechanical failure if not controlled. - EX. A swing in a playground can exhibit mechanical resonance. When you push the swing at the right frequency, it starts swinging more and more with each push. This is because the frequency of your pushes matches the natural frequency of the swing. 2. - - 3. - - Acoustic resonance Acoustic resonance is a specific type of mechanical resonance that occurs in sound waves. When an object or cavity vibrates at its natural frequency, it can produce and amplify sound waves of that same frequency. This phenomenon is responsible for the production of music in musical instruments like stringed instruments, wind instruments, and the resonance of sound in enclosed spaces like concert halls. EX. Musical instruments like a guitar or a violin rely on acoustic resonance. When you pluck a guitar string, it vibrates at its natural frequency, producing a specific musical note due to the resonance within the instrument's body. Electrical resonance Electrical resonance occurs in electrical circuits containing inductors, capacitors, and resistors. When the frequency of an alternating current (AC) source matches the natural resonant frequency of the circuit, it can lead to a significant increase in current or voltage. This phenomenon is used in various applications, including in radio tuning circuits and inductively coupled plasma (ICP) spectroscopy. EX. A common example is the tuning circuit in a radio. The LC (inductor-capacitor) circuit in the radio tuner resonates at the desired radio frequency. When the circuit is tuned to the correct frequency, it allows the radio to pick up the desired station by amplifying its signal while rejecting others. REPORT 3: BEAT What is beat? - Beat is a rhythmic pulsation that can be heard when two sound waves with slightly different frequencies are played together. It is created by the interference pattern between the two waves, which causes the amplitude of the resulting wave to oscillate at a frequency equal to the difference between the frequencies of the original waves. - In other words, beat occurs when two sound waves are out of phase with each other, causing them to alternately reinforce and cancel each other out. This creates a distinctive rhythmic pattern that can be heard as a pulsing or throbbing sound. Examples of beat Creating rhythm and pulse - Beat is a fundamental element of music that helps to create rhythm and pulse in songs. It provides a consistent underlying structure that allows listeners to tap their feet or dance along to the music. Drumming - In many genres of music, the drummer plays a crucial role in establishing and maintaining the beat. They often use a variety of techniques, such as syncopation and accenting, to create interesting and dynamic rhythms. Electronic music production - In electronic music production, beat is often created using software and digital instruments. Producers can manipulate the timing, velocity, and sound of each beat to create a unique and complex rhythm. The physics of sound and beat creation Sound oscillation and brain activity - Sound is created by the vibration of an object, which causes pressure waves in the air that our ears perceive as sound. These pressure waves are known as sound waves and can be analyzed in terms of their frequency and amplitude. - When two sound waves with slightly different frequencies overlap, they create a beat, which is a periodic variation in the amplitude of the sound wave. This beat can be heard as a pulsing or throbbing sound. - Research has shown that listening to beats with a frequency of around 10 Hz can entrain brain activity to a similar frequency, resulting in a relaxed or meditative state. This phenomenon is known as brainwave entrainment and has been studied for its potential therapeutic benefits. Analysis on sound oscillation and brain activity - Sound waves are created by the vibration of an object that travels through a medium such as air or water. These vibrations cause pressure changes in the medium which our ears perceive as sound. Sound can - be analyzed in terms of its frequency, amplitude, and wavelength. The frequency of a sound wave is measured in Hertz (Hz) and determines the pitch of the sound. Amplitude is the measure of the strength of the sound wave and determines the volume of the sound. Wavelength is the distance between two consecutive points on a sound wave that are in phase. When we hear a beat, it is actually the result of the brain processing two sound waves with slightly different frequencies. This phenomenon is known as binaural beats. When these two sound waves are presented to each ear separately, the brain processes them and produces a third tone which is the difference between the two frequencies. This third tone is what we perceive as the beat. Research has shown that exposure to binaural beats can have a positive effect on cognitive performance and mood. The mathematics of beat - When two sound waves with slightly different frequencies are played simultaneously, they create a phenomenon called beat. The frequency of the beat is equal to the difference between the frequencies of the two original waves. For example, if one wave has a frequency of 440 Hz and another has a frequency of 442 Hz, the beat frequency will be 2 Hz. - The formula for calculating beat frequency is simply the absolute value of the difference between the frequencies of the two waves. This can be expressed as: f_beat = |f1 - f2|. It's important to note that the amplitude of the beat is determined by the difference in amplitude between the two original waves. The greater the difference, the louder the beat will be. Musical applications - In music, beat is the underlying pulse or rhythm that drives a song forward. It's what makes you tap your foot or nod your head along to the music. Without beat, music would feel stagnant and lifeless. - One example of a song that utilizes beat is "Billie Jean" by Michael Jackson. The iconic drumbeat in the song creates a sense of urgency and excitement, driving the melody forward. Another example is "Stayin' Alive" by the Bee Gees. The disco beat in this song is so infectious that it's almost impossible not to dance along. Practical application - - One practical application of beat is in tuning musical instruments. When two notes played simultaneously are slightly out of tune, a beating sound can be heard. By adjusting the tuning of one of the notes, the beat frequency can be eliminated, resulting in a more harmonious sound. Another practical application of beat is in speech therapy. People who stutter or have difficulty with rhythm and timing in their speech can benefit from practicing with a metronome or other beat-keeping device. This can help improve their fluency and overall communication skills. Conclusion - - - In conclusion, we have explored the fascinating world of acoustics and the physics of sound. We have learned what beat is and how it is created, delved into the mathematics behind it, and examined its applications in both music and practical settings. Understanding the physics of sound and how it relates to beat is crucial not only for musicians and audio engineers but also for anyone interested in speech therapy or tuning instruments. By grasping these concepts, we can better appreciate the intricacies of the sounds around us and even improve our own auditory experiences. So let us continue to explore and learn about the science of sound, for as physicist and musician Albert Einstein once said, "The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science." REPORT 4: NATURE OF LIGHT What is Light? - Light is a form of energy that allows you to see the things around you. - Light is basic to almost all life on Earth. - Light is a form of electromagnetic radiation. How does light allow you to see things? - Light travels away from its source in straight lines. When it hits an object, it reflects (bounces off) and travels in a new direction. If the reflected light enters your eyes, you can see the object. Sources of Light: - All light comes from a luminous source. While non-luminous objects do not emit light but may reflect or transmit light from other sources. Whether, its natural or artificial. Materials Materials can indeed be classified based on how they respond to light incident on them. This classification typically involves three main categories. How does light travel? - LIGHT TRAVELS IN STRAIGHT LINES. When you shine a flashlight or torch at night, you can see those light travels in a straight path. LIGHT TRAVELS EXTREMELY FAST. It travels at the speed of 186,000 miles or 299,792 kilometers per second in a vacuum. A vacuum is an empty space so there is nothing that stops light from traveling. What are the 6 properties of light? ● Reflection of Light This property involves the bouncing back of light when it encounters a surface. The angle at which light strikes the surface is equal to the angle at which it is reflected. - ● Property: Reflection is the bouncing back of light waves when they encounter a surface. Example: A mirror reflects light, allowing you to see your own reflection. Refraction of Light Refraction is the bending of light as it passes from one medium into another, due to a change in its speed. ● Property: Refraction is the bending of light as it passes from one medium into another, due to a change in its speed. Example: When light passes from air into water, it bends, causing objects underwater to appear shifted from their actual position. Dispersion of Light Dispersion is the separation of light into its constituent colors (spectrum) based on the different wavelengths, resulting in a rainbow effect. - Property: Dispersion is the separation of light into its constituent colors (spectrum) based on the different wavelengths, resulting in a rainbow effect. Example: When white light passes through a prism, it separates into a spectrum of colors, as seen in a rainbow. Diffraction of Light Diffraction is the bending of light waves around obstacles or through narrow openings, causing them to spread out. - Property: Diffraction is the bending of light waves around obstacles or through narrow openings, causing them to spread out. Example: When light passes through a narrow slit, it diffracts, creating a pattern of light and dark bands on the other side. - Polarizing sunglasses reduce this reflection, known as glare. ● Interference of Light Interference occurs when two or more light waves overlap and combine, either constructively (amplifying) or destructively (canceling) each other. - Property: Interference occurs when two or more light waves overlap and combine, either constructively (amplifying) or destructively (canceling) each other. Example: In a soap bubble, interference between the incoming and reflected light waves creates the colorful patterns observed on its surface. Interference in soap bubbles occurs when light waves interact with each other as they pass through the thin film of soap solution that makes up the bubble's surface. When light from the sun or another light source hits the soap bubble, some of the light is reflected from the outer surface of the bubble, and some enters the bubble and is then reflected back from the inner surface. These two sets of reflected light waves can either reinforce each other (constructive interference) or cancel each other out (destructive interference), depending on their relative phases. This interference creates the beautiful and colorful patterns you often see on soap bubbles. The colors change as the thickness of the soap film changes, causing variations in the path lengths of the reflected light waves and, consequently, changes in the interference patterns and colors observed. This colorful phenomenon is a result of the interference of light waves and is a great example of the wave nature of light. These properties of light are fundamental in understanding its behavior and are utilized in various applications, from everyday phenomena like mirrors and rainbows to advanced technologies such as fiber optics and lasers. REPORT 5: ELECTROMAGNETIC SPECTRUM Colors of Light ● Polarization of Light Polarization refers to the orientation of the oscillations of light waves in a specific direction, restricting the vibration to a single plane. - Property: Polarization refers to the orientation of the oscillations of light waves in a specific direction, restricting the vibration to a single plane. Example: Polarized sunglasses use filters to block light waves vibrating in certain directions, reducing glare from surfaces like water or roads. Polarized lenses have a special chemical applied to them to filter light. The chemical's molecules are lined up specifically to block some of the light from passing through the lens. - Light is made up of wavelengths of light, and each wavelength is a particular color. The color we see is a result of which wavelengths are reflected back to our eyes. The color of light is determined by its wavelength. When white light, which contains all visible wavelengths, passes through a prism or a diffraction grating, it separates into its component colors, creating a spectrum. Electromagnetic Spectrum - The electromagnetic spectrum is the continuum of all electromagnetic waves, which are transverse waves composed of oscillating electric and magnetic fields propagating through space. - - These waves do not require a medium and can travel through a vacuum. The spectrum includes a vast range of wavelengths and frequencies, from the longest radio waves to the shortest gamma rays. The electromagnetic spectrum is divided into separate bands, and the electromagnetic waves within each frequency band are called by different names. The different types of electromagnetic radiation that make up the electromagnetic spectrum. Key Components of the Electromagnetic Spectrum: ● Radio Waves: Radio waves have the longest wavelengths in the spectrum, ranging from several millimeters to hundreds of meters. They are used in radio broadcasting, wireless communication, and radar systems. Radio waves are also emitted by stars and gasses in space. ● ● Microwaves: Microwaves have shorter wavelengths than radio waves, typically between a millimeter and a meter. They are used in microwave ovens, satellite communication, and certain wireless technologies. Infrared (IR) Radiation: Infrared radiation lies just beyond the visible spectrum, with wavelengths ranging from about 750 nanometers to 1 millimeter. It is used in heat sensing, remote controls, and infrared photography. Night vision goggles pick up the infrared light emitted by our skin and objects with heat. In space, infrared light helps us map the dust between stars. ● - Visible Light: Visible light is the portion of the spectrum that is visible to the human eye. It ranges from approximately 380 nanometers (violet) to 750 nanometers (red) and consists of various colors. Visible light may be a tiny part of the electromagnetic spectrum, but there are still many variations of wavelengths. We see these variations as colors. On one end of the spectrum is red light, with the longest wavelength. Violet light has the shortest wavelength. White light is a combination of all colors in the color spectrum. It has all the colors of the rainbow. The colors of the visible light spectrum can be remembered by the mnemonic "Roy G Biv" for red, orange, yellow, green, blue, indigo, and violet. ● Ultraviolet (UV) Radiation: UV radiation has shorter wavelengths than visible light, ranging from 10 to 400 nanometers. It has applications in disinfection, forensics, and astronomy. Ultraviolet radiation is emitted by the Sun and are the reason skin tans and burns. "Hot" objects in space emit UV radiation as well. UV energies are too high for human eyes to see. UV light traces the hot glow of stellar nurseries and is used to identify the hottest, most energetic stars. ● X-Rays: X-rays have very short wavelengths, typically between 0.01 to 10 nanometers. They are used extensively in medical imaging, materials analysis, and airport security. X-rays come from the hottest gas that contains atoms. They are emitted from superheated material spiraling around a black hole, seething neutron stars, or clouds of gas heated to millions of degrees. A dentist uses X-rays to image your teeth, and airport security uses them to see through your bag. Hot gasses in the Universe also emit X-rays. ● Gamma Rays: Gamma rays have the shortest wavelengths and highest frequencies in the spectrum, measuring less than 0.01 nanometers. They are produced in nuclear reactions and are used in cancer treatment and astrophysics. Gamma rays have the highest energies and shortest wavelengths on the electromagnetic spectrum. They come from free electrons and stripped atomic nuclei accelerated by powerful magnetic fields in exploding stars, colliding neutron stars, and supermassive black holes. Ionizing Radiation - - Energy Levels: Ionizing radiation has very high energy levels Examples: Types of ionizing radiation include X-rays, gamma rays, and certain particles like alpha and beta particles. Effect on Matter: Ionizing radiation can ionize atoms and molecules by stripping away tightly bound electrons, creating charged ions. This can damage or alter the chemical structure of materials and biological tissues. Health Risks: Exposure to ionizing radiation carries health risks, including an increased risk of cancer and damage to DNA. Non-Ionizing Radiation - - Energy Levels: Non-ionizing radiation has lower energy levels, with longer wavelengths compared to ionizing radiation. Examples: Types of non-ionizing radiation include visible light, infrared (IR), UV rays, microwaves, and radio waves. Effect on Matter: Non-ionizing radiation does not have enough energy to ionize atoms or molecules. It can, however, cause heating effects when absorbed by materials (e.g., microwave ovens heat food). Health Risks: Non-ionizing radiation is generally considered safe at typical exposure levels. Significance and Applications ● ● ● ● ● ● ● Communication Medicine Scientific Research Consumer Electronics Security and Defense Technological Innovation Exploration of the Universe REPORT 6: REFLECTION Geometric Optics - Our lives are filled with light. light can evoke spiritual emotions. Life itself could not exist without light’s energy. Optics is the branch of physics that deals with the behavior of visible light and other electromagnetic waves. It has two major parts based on the size of objects that light encounters: geometric optics, which deals with interactions with objects that are larger than the light's wavelength, and wave optics, which deals with interactions with smaller objects. Ray Aspect of Light 1. 2. 3. Light reaches the upper atmosphere of Earth traveling through empty space directly from the source. Light can travel through various media, such as air and glass, to the person. Light can also arrive after being reflected, such as by a mirror. Two laws govern how light changes direction when it interacts with matter: 1. 2. Law of reflection, for situations in which light bounces off matter. Law of refraction, for situations in which light passes through matter. Law of Reflection Whenever we look into a mirror, or squint at sunlight glinting from a lake, we are seeing a reflection. Large telescopes use reflection to form an image of stars and other astronomical objects. The law of reflection shows how the angles are measured relative to the perpendicular to the surface at the point where the light ray strikes. Key Components of Reflection 1. Incident Ray 2. Refracted Ray 3. Normal Line 4. Angle of Incidence (i) 5. Angle of Refraction (r) From a less dense to a denser medium example: from air to glass From a denser to a less dense medium example: from water to air Refraction in Water - Light rays change direction at the surface of the water. - The image of the chest appears to be more shallow than the actual chest Refraction of Light If ray of light enters from rare into denser medium it bends towards the normal. But when it enters from denser into rare medium it bends away from normal Practical Application of Refraction Optics: Lenses, such as those in eyeglasses or cameras, rely on refraction to focus light and correct vision or capture images. Astronomy: Refraction by Earth's atmosphere affects the apparent position of celestial objects, leading to phenomena like atmospheric dispersion and the Green Flash. Prism Spectroscopy: Prisms use refraction to disperse light into its constituent colors, enabling the study of spectra and the identification of elements in stars. Mirage Formation: Refraction of light in the Earth's atmosphere causes mirages, where distant objects appear distorted or displaced. Underwater Vision: Snorkelers and divers experience refraction when light passes from water into air, making objects underwater appear closer and larger than they are REPORT 8: PLANE MIRRORS REPORT 9: SPHERICAL MIRRORS REPORT 7: REFRACTION What is Refraction? - The bending of light rays as they pass between two different media - Refraction occurs due to changes in speed of light in different mediums - Different media slow down light by different amounts the more that light slows down, the more the light is refracted.