Oscillations, Periodism and Pendulums

Oscillations and Periodism

• Oscillation involves a periodic change in a physical quantity, shifting from equilibrium and returning
• Oscillations can be mechanical, electromagnetic, or thermal
• Periodism is vital for organisms, influencing many oscillations

Periodic Processes in Organisms

• Insulin secretion happens every 5–6 minutes
• Heart pumping and breathing occur periodically
• Melatonin secretion has a periodic nature
• Sound production in the mouth varies with air pressure
• Body temperature lowers to its maximum in the mornings around 5:00 a.m.

Mechanical Oscillating Systems

• Mechanical oscillating systems have components like a massless rod, a bob(weight), and earth, as seen in mathematical pendulums
• Systems can be affected by internal and external forces if not isolated

Mathematical Pendulum: Internal Forces

• The internal forces acting on a mathematical pendulum are Earth's gravitational pull and cord tension

Period and Frequency of a Pendulum

• Displacing the bob causes the gravitational force and cord tension to become unbalanced
• Time for one full oscillation = period
• Frequency is the number of oscillation cycles per unit of time
• Frequency is measured in Hertz when time is in seconds

Types of Oscillations

• Free oscillation occurs with only internal forces
• Forced oscillation involves both internal and external forces
• Free oscillations are damped due to air friction, reducing amplitude over time but frequency remains constant
• Forced oscillations are non-damped with enough periodic external force

Simple Harmonic Motion

• Simple harmonic motion has a restoring force directly proportional and opposite to the direction of displacement
• Obeys sine or cosine rules

Energy in Oscillating Systems

• Total internal energy is the sum of potential and kinetic energy
• Potential energy is highest when amplitude is greatest, but kinetic energy is zero
• Kinetic energy increases when the object moves toward its resting state, decreasing potential energy
• Potential energy is zero at the system's center, while kinetic energy is at its maximum

Damping Ratio

• Damping ratio measures of how quickly oscillations decrease in amplitude
• Logarithmic decrement of damping: the ratio of the amplitudes of any two successive peaks

Resonance

• Resonance is when a system oscillates with greater amplitude at certain frequencies
• The maximum response amplitude frequencies are called resonant frequencies
• Resonance occurs when oscillating system's internal frequency equals to external oscillation's frequency
• Resonance poses danger when infrasound causes enough vibration to damage organs

Auto-oscillations

• Auto-oscillations (self-oscillations) has energy stored in the system itself
• This also has pre-set points on when energy is used, and frequencies to use to maintain its original frequency

Mechanical Waves

• Mechanical oscillation propagation in a discrete, elastic medium = mechanical wave
• Energy transfers to neighboring particles, causing them to oscillate
• Particles stay in place, but energy shifts
• Mechanical waves can be categorized as longitudinal or transverse
• Longitudinal waves oscillate along the propagation direction
• Transverse waves oscillate perpendicular to the wave's propagation
• Sound waves are longitudinal

Wave Measurements

• Wavelength is the distance between identical points on two waves
• Corresponds to the time period for one full oscillation
• Amplitude is the displacement measure from a wave's rest position

Wave Properties

• Basic properties of waves are interference, diffraction, reflection, and refraction
• Interference amplifies or partially cancels waves when two or more coherent waves are superposed
• Coherent waves have a permanent phase difference or are in the same phase

Wave Interference

• Constructive interference amplifies the resulting wave
• Destructive interference weakens or cancels the resulting wave

Diffraction

• Diffraction: wave property through which a wave can overcome obstacles in its path by bending

Reflection

• Reflection reflects an incident wave from a border of two media
• Incidence angle is reflection angle

Refraction

• Refraction: wave property where waves change direction and speed when passing through different mediums
• Snell's Law describes the relationship between incidence and refraction angles

Wavefronts

• Wavefronts form when particles oscillate, oscillations spread in all directions from the initial oscillating particle

Sound Waves

• Sound waves are mechanical and longitudinal
• Require a discrete, elastic medium
• Cannot travel in a vacuum

Types of Sound Waves

• Musical sound is also known as a tone
• Simple tone = only one frequency
• Complex tone = several simple tones of different frequencies
• Noise is a complex, non-repeating pattern, different from complex tone
• Sound blasts are short, highly intensive sound waves

Sound Parameters

• Physical attributes include wavelength, frequency, amplitude, propagation speed, impedance, and intensity
• Watt is energy conversion/transfer rate
• Intensity: 1 Watt / 1 square meter
• Rayleigh: unit of impedance
• Speed depends on temperature
• Higher temperature produces higher propagation speed
• Sound travels slower at high altitudes
• Faster in solids than in liquids or gases

Sound Spectrum

• Infrasound: <20Hz
• Acoustic sound: 20-20000 Hz
• Ultrasound: >20000Hz
• Only acoustic waves are audible to humans

Auditory System

• Acoustic waves start in the trachea during exhalation
• Mouth acts as a resonator
• Amplifies sound through changes in mouth volume
• Outer ear gathers and directs waves to the ear canal(external auditory canal)
• Middle ear intensifies the sound by funneling waves to the smaller ear drum
• Converts to mechanical vibrations via the auditory ossicles (hammer, anvil, and stirrup)
• Transfers to the oval window of the inner ear
• Middle ear muscles contract when intensity is too high
• In the inner ear round window membrane vibrates in the opposing direction
• More energy is needed to cause vibrations of basilar membrane near oval window and therefore only high frequency (acoustic) waves cause those vibrations
• With increased distance from the oval window, the basilar membrane becomes wider and more relaxed, resulting in less energy and lower frequency
• When intensity and amplitude of waves are higher
• More hair cells are vibrated and depolaraized(via basilar membrane)
• Which leads to a stronger signal transmission to brain.

Sound Measurement

• Intensity is measured in Bels or decibels
• 1 bel equals logarithmic ratio of intensity to reference intensity = 10^-12 watt/m²
• Measured as loudness perceived by humans in phons

Medical Applications

• Stethoscopes: Hear internal body sounds
• Phonocardiography: Records heart work and blood circulation sounds

Ultrasound Waves

• Ultrasound has a frequency >20000Hz
• Humans can't hear ultrasound
• It can cause effects when introduced via skull
• This it the hypersonic effect
• Bats use ultrasound to navigate, which is called echolocation

Ultrasound Uses

• Diagnostics and physical therapy applications
• Diagnostics via ultrasonography
• Used to identify structural changes of tissue
• Nature and location determined through distance
• Used to identify tissue acoustic density
• Used to identify speed of moving objects through frequency change

Ultrasound Physical Therapy

• Thermal effects
• Cavitation, mostly stable, is useful for drug penetration and kidney stone breakage
• Microcurrents

Cavitation

• Cavitation can present in two forms
• Stable, or unstable
• cavitation is the formation of micro bubbles in liquids
• water is primary example
• Is due to pressure distribution asymmetry

Doppler Effect

• Doppler effect happens when source wave frequency doesn’t match registered frequency by observer
• Can determine the speed of red blood cells movement

Infrasound Waves

• Infrasound waves have frequency <20Hz
• Natural sources: storms, volcanos, earthquakes
• Artificial sources: motors, ventilators, compressors
• Can cause a wide array of mental and physical effects to humans
• Also used as a massaging means for tissues within medicine applications

Important Formulas

• v=s/t = λ/T
• λ = v/v
• x=vT
• Ṽ = 1/T