Physics Study Notes: Waves, Sound, and Electromagnetic Radiation

Definitions and Types of Pulses

Following the study of physics, a pulse is defined as a single disturbance in a medium. Pulses are categorized into two main types based on the direction of particle movement relative to the direction of the pulse’s motion. A transverse pulse is a pulse in which the particles of the medium move perpendicularly (at right angles) to the direction of the pulse's movement. These pulses are typically created by an up-and-down or left-and-right motion. In contrast, a longitudinal pulse is a pulse where the particles of the medium move parallel to the direction of the pulse’s motion. This type of pulse is generated through a push-pull vibration.

Characteristics of Pulses and Waves

Several terms are essential to describing the physical properties of pulses and waves. The amplitude is defined as the maximum displacement of a particle from its rest position, also known as the equilibrium position. The pulse length refers to the total distance between the beginning and the end of a single pulse. The rest position is the baseline position from which all particles begin their displacement and to which they eventually return. In the context of longitudinal waves, specific regions are identified as verdigting (compression), which is a region of high pressure, and verdunning (rarefaction), which is a region of low pressure.

Superposition and Interference of Pulses

The phenomenon known as superposition of pulses involves the algebraic sum of the amplitudes of two pulses that occupy the same space at the same time. This interaction is called interference. Constructive interference occurs when the crest of one pulse overlaps with the crest of another pulse, resulting in a single pulse with an increased amplitude. Destructive interference occurs when the crest of one pulse overlaps with the trough of another pulse, resulting in a pulse with a decreased or neutralized amplitude. Once the pulses have passed through each other, they continue along their original path with their original properties unchanged, such as their initial amplitude.

Fundamental Wave Properties and Terminology

A wave is defined as a series of successive pulses. Transverse waves consist of crests, which are the highest points on the wave, and troughs (or dales), which are the lowest points. The amplitude ( $A$ ) remains the maximum displacement from equilibrium. The wavelength ( $\lambda$ ) is the distance between any two consecutive points that are in phase. Points are considered in phase if they are in the exact same state of vibration. Conversely, points are out of phase if they are in different states of vibration.

Frequency ( $f$ ) is defined as the number of wave pulses passing a point per second. The formula for frequency is:

$f = \frac{n}{t}$

Where $n$ is the number of waves and $t$ is the time. Frequency can also be related to the period ( $T$ ) by the equation:

$f = \frac{1}{T}$

The period ( $T$ ) is the time required for one complete wave pulse to occur. The relationship is expressed as:

$T = \frac{t}{n}$

$T = \frac{1}{f}$

Frequency is inversely proportional to the period. Wave speed ( $v$ ) is the distance a point on the wave moves per unit of time. It is calculated using the wave equation:

$v = f \times \lambda$

Alternatively, it can be calculated using the general speed formula:

$v = \frac{D}{t}$

Nature and Transmission of Sound Waves

Sound waves are longitudinal waves created by vibrations that produce regular variations in pressure within a medium. The anatomy of the ear, including the Pinna, Ear canal, Eardrum, Middle Ear (3 bones), Cochlea, and Nerve, facilitates the hearing of these pressure changes. The speed of sound is determined by two primary factors: the elasticity of the medium and the density of the medium. Elasticity describes the stiffness of the medium and how quickly particles return to their original positions; higher elasticity leads to a faster sound speed. Consequently, sound travels fastest in solids, followed by liquids, and slowest in gases. Regarding density, particles in a warm medium have more kinetic energy and return to their positions faster than those in a cold medium, meaning sound travels faster in warm air or water than in cold.

Properties and Applications of Sound

Pitch refers to how high or low a sound is perceived and is determined entirely by the frequency of the wave. Loudness (also called hardness) is determined by the amplitude. A louder sound has greater compression in the wave, though frequency, wavelength, and speed remain constant. Loudness is measured in decibels ( $dB$ ), and exposure to levels above $85\,dB$ can lead to permanent hearing loss. Quality (or tone) allows one to distinguish between two notes of the same pitch and loudness played on different instruments due to their different waveforms. Humans can hear sounds within the audible range of $20\,Hz$ to $20\,000\,Hz$ ( $20\,kHz$ ). Sounds below $20\,Hz$ are called infrasound and are used to monitor volcanic eruptions, tsunamis, and nuclear explosions. Sounds above $20\,kHz$ are called ultrasound.

Ultrasound is used for sonar imaging because it has a much shorter wavelength. When ultrasound hits a barrier, part of it is reflected, part is absorbed, and part is transmitted. Reflected ultrasound is used in medical imaging (scans) as it does not damage soft tissue. It is also used by physiotherapists to reduce swelling, to break up kidney stones, for pregnancy monitoring, for navigation in the dark (by bats), for locating fish, and for determining the depth of the ocean.

Nature and Properties of Electromagnetic (EM) Radiation

Electromagnetic radiation is formed by accelerating charges which create oscillating electric and magnetic fields at right angles to each other and to the direction of propagation. EM waves have several distinct properties: they travel at a constant speed of $c = 3 \times 10^8\,m/s$ in a vacuum, require no medium for propagation, and possess all the properties of transverse waves. EM radiation exhibits wave-particle duality, meaning it has both wave and particle characteristics. A photon is defined as a "packet" or quantum of energy found in light/EM radiation. The energy of a photon ( $E$ ) in Joules ( $J$ ) is directly proportional to the frequency and is calculated using Planck's constant ( $h = 6.63 \times 10^{-34}\,J \cdot s$ ):

$E = h \times f$

Because $c = f \times \lambda$ , the energy can also be calculated as:

$E = \frac{h \times c}{\lambda}$

The Electromagnetic Spectrum

The EM spectrum consists of all frequencies of electromagnetic radiation arranged in order. Higher frequency waves have shorter wavelengths and carry more energy, making them more hazardous to humans. The spectrum, in order from longest wavelength/lowest frequency to shortest wavelength/highest frequency, includes:

Radio waves: Used for radio and television broadcasts and radio telescopes. A negative effect is noise pollution from loud devices.
Microwaves: Used for telephone and cellphone connections, communication satellites, radar systems, and microwave ovens. Self-phone use can become addictive.
Infrared (IR): Used in remote controls and optical fibers. Can be exploited by intruders/looters using specialized equipment.
Visible light: Reflected and refracted light allow vision and enable photosynthesis.
Ultraviolet (UV): Used for sterilizing food and equipment, security scanning, and lengthening food shelf-life. Overexposure can cause eye damage and skin cancer.
X-rays: Used for CT scans and security scanners. Can damage skin and underlying tissue.
Gamma rays: Used for cancer radiation treatment and nuclear radiation. These can cause severe tissue damage.

Questions & Discussion

Question: A wave wherein particles vibrate perpendicularly to the path of the wave is produced by which device? Response: An X-ray machine creates such a transverse wave, unlike a bat, car hooter, or ambulance which produce longitudinal sound waves.

Question: Calculate the speed of sea waves reaching a wall at six waves in $4\,s$ with a wavelength of $10\,m$ . Response: First determine frequency: $f = \frac{6}{4} = 1.5\,Hz$ . Then speed: $v = f \times \lambda = 1.5 \times 10 = 15\,m/s$ . (Note: Calculations in the specific worksheet example used rounded figures leading to $14.9\,m/s$ if using the period $0.67\,s$ ).

Question: What is the result of two pulses of $1.8\,m$ and $1.2\,m$ amplitudes meeting at point R while moving toward each other? Response: If they are in opposition (destructive interference), the resulting amplitude is $1.8 - 1.2 = 0.6\,m$ .

Question: Why does the speed of sound differ in air ( $340\,m/s$ ) compared to seawater ( $1480\,m/s$ )? Response: Sound in air is slower because air is less dense and less elastic than water. The particles in water are closer together, allowing the vibration to pass more quickly.

Question: Calculate the energy of a photon for a radio wave with a wavelength of $3\,m$ . Response: First, find frequency: $3 \times 10^8 = f \times 3 \implies f = 1 \times 10^8\,Hz$ . Then energy: $E = (6.63 \times 10^{-34})(1 \times 10^8) = 6.63 \times 10^{-26}\,J$ .