🫴Physical Science Unit 11 – Waves and Sound

What Are Waves?

• Waves are disturbances that transfer energy through a medium without transferring matter
• Waves can travel through various media such as water, air, and solid materials
• Waves are created when a source of energy causes a disturbance in a medium
  • For example, dropping a pebble into a pond creates ripples (waves) on the water's surface
• Waves are characterized by their amplitude, wavelength, frequency, and speed
• Waves can be transverse or longitudinal depending on the direction of the disturbance relative to the direction of wave propagation
• Waves follow the principle of superposition, meaning they can pass through each other without being disturbed
• Waves can be reflected, refracted, or diffracted when they encounter boundaries or obstacles

Types of Waves

• Mechanical waves require a medium to propagate and include water waves, sound waves, and seismic waves
  • These waves transfer energy through the medium by causing particles to oscillate
• Electromagnetic waves do not require a medium and include light, radio waves, X-rays, and gamma rays
  • These waves are created by oscillating electric and magnetic fields and can travel through a vacuum
• Transverse waves have particle motion perpendicular to the direction of wave propagation (e.g., light waves, water waves)
• Longitudinal waves have particle motion parallel to the direction of wave propagation (e.g., sound waves, pressure waves)
• Surface waves, such as water waves and seismic waves, travel along the boundary between two media
• Standing waves occur when two identical waves traveling in opposite directions interfere, creating a stationary pattern (e.g., on a guitar string)

Wave Properties

• Amplitude is the maximum displacement of a wave from its equilibrium position and determines the energy carried by the wave
• Wavelength is the distance between two consecutive crests or troughs of a wave
  • Wavelength is typically represented by the Greek letter lambda ($\lambda$)
• Frequency is the number of wave cycles that pass a fixed point per unit time, usually measured in hertz (Hz)
  • Frequency is inversely proportional to wavelength: $f = \frac{v}{\lambda}$, where $f$ is frequency, $v$ is wave speed, and $\lambda$ is wavelength
• Period is the time taken for one complete wave cycle to occur, measured in seconds (s)
  • Period is the reciprocal of frequency: $T = \frac{1}{f}$, where $T$ is period and $f$ is frequency
• Wave speed is the distance a wave travels per unit time and depends on the properties of the medium
  • Wave speed is calculated using the equation: $v = f\lambda$, where $v$ is wave speed, $f$ is frequency, and $\lambda$ is wavelength
• Phase is the position of a point on a wave cycle relative to its origin

Sound Waves Explained

• Sound waves are longitudinal mechanical waves that propagate through a medium by causing compression and rarefaction of particles
• Sound waves are created by vibrating objects, such as vocal cords or musical instruments
• The speed of sound depends on the medium and its properties (e.g., temperature, density, and elasticity)
  • In air at 20°C (68°F), the speed of sound is approximately 343 m/s (1,125 ft/s)
• The human audible frequency range is typically between 20 Hz and 20,000 Hz
  • Frequencies below 20 Hz are called infrasound, while those above 20,000 Hz are called ultrasound
• Sound waves with higher amplitudes are perceived as louder, while those with higher frequencies are perceived as higher-pitched
• Sound waves can be reflected (echoes), refracted (when passing through different media), or diffracted (bending around obstacles)
• The Doppler effect is the apparent change in frequency of a sound wave when the source or observer is moving relative to each other

How We Hear

• The human ear consists of three main parts: the outer ear, middle ear, and inner ear
• Sound waves are collected by the outer ear (pinna) and directed through the ear canal to the eardrum (tympanic membrane)
• The eardrum vibrates in response to the sound waves, transmitting the vibrations to the three tiny bones (ossicles) in the middle ear: the malleus, incus, and stapes
• The ossicles amplify the vibrations and transfer them to the oval window, which leads to the fluid-filled cochlea in the inner ear
• The vibrations create waves in the cochlear fluid, causing the basilar membrane to ripple
  • Different frequencies stimulate different parts of the basilar membrane, allowing for frequency discrimination
• Hair cells along the basilar membrane convert the mechanical vibrations into electrical signals that are sent via the auditory nerve to the brain for processing and interpretation

Measuring Sound

• Sound intensity is the power carried by sound waves per unit area, measured in watts per square meter (W/m²)
• Sound intensity level (SIL) is a logarithmic measure of sound intensity relative to a reference level, expressed in decibels (dB)
  • The reference level is typically the threshold of human hearing, which is 10⁻¹² W/m²
  • The formula for SIL is: $SIL = 10 \log_{10} \frac{I}{I_0}$, where $I$ is the sound intensity and $I_0$ is the reference intensity
• The decibel scale is logarithmic, meaning a 10 dB increase represents a tenfold increase in sound intensity
  • A 3 dB increase represents a doubling of sound intensity
• Sound pressure level (SPL) is another logarithmic measure of sound, comparing the root mean square (RMS) pressure of a sound to a reference pressure
  • The reference pressure is typically 20 µPa, which is the threshold of human hearing
• Loudness is the subjective perception of sound intensity and depends on factors such as frequency, duration, and individual sensitivity

Wave Interactions

• Reflection occurs when a wave encounters a boundary and bounces back, with the angle of incidence equal to the angle of reflection
  • Examples include echoes and the reflection of light by mirrors
• Refraction is the bending of waves as they pass from one medium to another with a different speed
  • Refraction is caused by a change in the wave's speed and is governed by Snell's law: $\frac{\sin \theta_1}{v_1} = \frac{\sin \theta_2}{v_2}$, where $\theta$ is the angle and $v$ is the wave speed
• Diffraction is the bending of waves around obstacles or through openings
  • The amount of diffraction depends on the wavelength and the size of the obstacle or opening
• Interference occurs when two or more waves overlap, resulting in a new wave pattern
  • Constructive interference occurs when waves are in phase, resulting in an increased amplitude
  • Destructive interference occurs when waves are out of phase, resulting in a decreased amplitude
• Resonance is the phenomenon where a system oscillates with greater amplitude at specific frequencies called resonant frequencies
  • Resonance can be observed in musical instruments, tuning forks, and the collapse of the Tacoma Narrows Bridge in 1940

Real-World Applications

• Ultrasound imaging uses high-frequency sound waves to create images of internal body structures (e.g., during pregnancy)
• Sonar (sound navigation and ranging) uses sound waves to detect and locate objects underwater, such as in submarine navigation and fish finders
• Seismic waves, generated by earthquakes or artificial explosions, are used in geophysical exploration to map subsurface structures and locate oil and gas reserves
• Noise-canceling headphones use destructive interference to reduce ambient noise by generating sound waves with the same amplitude but opposite phase
• Acoustic design in architecture involves controlling sound reflection, absorption, and diffraction to optimize the acoustic properties of concert halls, recording studios, and other spaces
• Doppler radar uses the Doppler effect to measure the velocity of moving objects, such as weather systems or speeding vehicles
• Sonic and ultrasonic cleaning use high-frequency sound waves to remove dirt and contaminants from objects, such as jewelry and surgical instruments
• Acoustic levitation uses standing waves to suspend small objects in mid-air, with potential applications in material processing and containerless experiments