Sound and Waves Reading material

Waves and Sound

• Information about physical surroundings primarily reach individuals through hearing and sight.
• Sound and light are different phenomena but both are waves which transmit information without physical contact.
• A wave is a disturbance carrying energy from one location to another without mass transfer, stimulating sensory mechanisms.
• The properties of sound and general wave motion, the process of hearing and other biological aspects of sound are explained

Properties of Sound

• Sound is a mechanical wave generated by vibrating objects
• Vibrating objects disturb surrounding air molecules, causing them to move which cause adjacent molecules to propagate the disturbance away from the source
• Air vibrations reach the ear, vibrating the eardrum, and producing nerve impulses interpreted by the brain.
• All matter transmits sound to some extent, requiring no material medium for the sound to propagate from the source to the receiver
• The bell-in-a-jar experiment demonstrates that sound needs a material medium
• When the bell is set in motion, its sound is audible, but as air is evacuated, the sound diminishes until inaudible.
• Propagating disturbance in a sound-conducting medium comes as alternating compressions and rarefactions due to a vibrating source
• Compressions and rarefactions involves deviations in the medium's density from its average value
• Variations in density are equivalent to pressure changes in a gas.
• Sound intensity is determined by compression and rarefaction magnitude in the propagating medium
• Frequency is determined by the rate of compressions and rarefactions, measured in cycles per second or Hertz (Hz)
• 1 Hz equals 1 cycle per second
• Vibrational motion of objects can be complex, resulting in complex sound patterns, which can be analyzed using simple sinusoidal vibrations, such as those from a tuning fork.
• Pure tone: A sound pattern in which pressure variations from compressions and rarefactions are sinusoidal when propagating through air
• Wavelength (λ): the distance between nearest equal points on a sound wave
• Sound wave speed (v) depends on the material, averaging 3.3 × 10^4 cm/sec in air at 20°C , and roughly 1.4 × 10^5 cm/sec in water
• Relationship between frequency, wavelength, and speed shown: v = λf which applies to all types of wave motions.
• The total pressure in a sinusoidal sound wave's path is P = Pa + Po sin 2πft

Wave Properties

• Pa: ambient air pressure at sea level at 0°C equals 1.01 × 10^5 Pa equals 1.01 × 10^6 dyn/cm²
• Po: maximum pressure change from the sound wave
• f: the frequency of the sound
• Intensity (I): amount of energy transmitted by a sinusoidal sound wave per unit time through each unit area perpendicular to the direction of sound propagation
• Intensity is given by: I= Po^2 / 2pv
• p: density of the medium
• v: speed of sound propagation
• Reflection, refraction, interference, and diffraction are wave characteristics that play a vital role in seeing and hearing

Properties of Waves

• A wave reflects/enters into the medium when it passes from one medium to another
• Reflection is:
• Specular (mirror-like) when the interface between media is smooth relative to the wavelength (irregularities smaller than λ)
• Diffuse reflection when the surface irregularities are larger than the wavelength
• Refraction: when a wave hits interface at an angle and the direction of the transmitted wave changes to a new medium
• The angle of reflection always equals the angle of incidence.
• The angle of the refracted wave relies on the properties of the media, determining fraction of energy transmitted from one area to the other
• The ratio of transmitted to incident intensity = It/Ii = 4ρ1v1ρ2v2 / (ρ1v1 + ρ2v2)^2(for a sound wave hitting perpendicular to the interface)
• ρ1, v1, ρ2, v2: densities and velocities in the two media.
• Only 0.1% of sound energy enters (99.9% reflected) when sound travels from air to water perpendicularly to the surface; water is an efficient barrier to sound
• Interference: The total disturbance in a medium where two or more waves simultaneously travel
• Constructive interference: adding of two waves that are in phase, increasing the wave disturbance.
• Destructive interference: reducing the wave disturbance by two waves out of phase by 180°
• Wave disturbance is cancelled completely if magnitudes of two out-of-phase waves that are the same
• Standing wave: stationary pattern produced by two equal frequency/magnitude waves moving opposite directions; only exist at resonant frequencies.

Diffraction and the Ear

• Diffraction: Waves spread as they travel through a medium
• Spreading occurs when a wave meets an object
• Diffraction relies on wavelength, where longer wavelengths equals increased spreading.
• Significant diffraction occurs if the obstruction size is less than the wavelength.
• Light and sound waves can be focused using curved reflectors and lenses
• The diameter of the focused spot cannot be smaller than about λ/2
• Hearing is produced by the ear nerves reacting to pressure changes

The Ear

• Ear nerves are pressure sensitive, but the ear detects pressure better than other parts of the body
• The ear is divided into outer, middle, and inner sections
• the sensory cells (convert sound to nerve impulses) in the liquid-filled inner ear
• Outer and middle ear purpose: conduct sound to inner ear
• Outer ear: pinna (external flap) and ear canal, ends at tympanic membrane (eardrum).
• The pinna has limited ability to help humans locate sources of sound
• Adult's ear canal averages 0.75 cm in diameter and 2.5 cm in length.
• Provides resonance around 3000 Hz, which explains ear sensitivities to sound
• Air-to-inner ear fluid sensory cell coupling is necessary for sound perception.
• Direct sound wave coupling into fluid is inefficient because energy is reflected at the interface
• Middle ear provide the route for sound waves from air to the inner ear fluid
• Middle ear: ossicles, a linkage of three connecting the eardrum to the inner ear air-filled cavity: malleus (hammer), incus (anvil), and stapes (stirrup).
• Sound waves vibrate the eardrum, which transmit vibrations to the oval window
• Middle ear muscles control volume by connecting the ossicles to the walls.
• If the sound is too loud, these muscles tense to stiffen the eardrum and reduce sound transmission.
• The middle ear isolated the inner ear from disturbances created by head movements, chewing, and one’s own voice
• The Eustachian tube links the middle ear with the upper throat, maintaining atmospheric pressure in the middle ear.
• Swallowing moves air through the Eustachian tube
• Rapid air pressure changes causes eardrum imbalance, causing sensation and pain
• Pain occurs when the Eustachian tube is blocked from swelling or infection
• Nerve impulses occur from sound waves via the cochlea located in the inner ear
• the spiral-shaped canal contains the oval and round windows
• The cochlea is formed into a spiral with about 2 ¾ turns, and averages about 35mm uncoiled
• Three parallel ducts are inside the cochlea, called the vestibular/tympanic canals at the helicotrema, and cochlear duct

Ear Performance

• The basilar membrane supports the auditory nerves
• the round window at the tympanic canal dispenses excess sound wave energy via motion
• Auditory nerve impulses create subjective sensations: loudness, pitch and quality
• Complex sound wave patterns are analyzed into simple sine waves of different frequencies which are added together
• sounds have fundamental frequency and harmonics
• The harmonic content differentiates sound sources.

Frequency, Intensity, and Loudness

• Human ears detect sound at frequencies of 20-20,000 Hz, but the ear is most sensitive between 200-4000 Hz, which decreases at higher/lower frequencies
• Some people cannot hear sounds at 8000 Hz+, whichhearing deteriorates with age.
• Sound pitch relates to sound frequency which increases with it; middle C is 256 Hz, and A above is 440 Hz
• The ear responds to a wide intensity range
• Threshold of hearing: 10^-16 W/cm^2 (lowest intensity) at 3000 Hz
• Threshold of pain: 10^-4 W/cm^2(loudest tolerable sound)
• Sound intensities above the threshold of pain cause permanent eardrum/ossicle damage
• The ear responds non-linearly to sound intensity and is closer to logarithmic
• Sound intensity is measured on a logarithmic scale relative to 10^-16 W/cm2 which is measured in decibels (dB)

Logarithmic Intensity

• Logarithmic Intensity = 10log (Sound intensity in W/cm^2 / 10^-16 W/cm^2)
• A logarithmic response provides a useful guide for assessing the sensation of loudness
• At the hearing threshold of about 2000-3000 Hz, the ear can detect 10^-16 W/cm^2, corresponding to approximately 2.9 × 10^-4 dyn/cm^2 which is super sensitive
• Random air pressure variations from thermal motion of molecules average about 0.5 × 10−4 dyn/cm2
• Ear sensitivity approaches maximum limit at which air noise fluctuations are detected.
• Ear molecule displacement at the threshold is less than size of the molecules
• Ear is sensitive due to the mechanical construction that amplifies sound pressure
• Middle ear amplifies pressure
• Eardrum averages 30x bigger than the oval window which allows increased pressure multiplication
• Ossicles use levers, a mechanical advantage with mechanical advantages
• Pressure is increased due to ear canal resonance in 3000 Hz range
• Formula: The total sound pressure mechanical amplification within the 3000 Hz range = 2 × 30 × 2 = 120, amplifying intensity by almost 14,400x.
• The brain:filters out noise and allows meaningful sounds from louder surroundings and suppress meaningless sounds

Bats, Animals, and Sound

• Human auditory organs are developed, but some animals like bats can hear better by emitting/receiving frequencies
• Sense of hearing is so acute that they can obtain information from echoes which is in many ways as detailed as sight information.
• The Vespertilionidae bats family emit short chirps for about 3 msec, in 70 msec intervals starting at 100 * 10^3 Hz, that lessens to 30 * 10^3 Hz
• Bat ears respond to these high frequencies
• Spaces that contain chirps that allow the bat to hear weak echos and determine distance
• Changes that contain echo frequencies which help the bat estimate sizes and object location
• A 70 msec spacing, echo from 11.5 m object is found before next chirp.
• Experiments show bat echolocation can avoid 0.1 mm wire obstacle, according to wave diffraction.
• Porpoises, whales, and birds use echoes to locate objects better than bats
• Animals (insects, rattlesnakes)produce sound various ways, but most use respiratory systems
• Vocal cords are located in the upper trachea of humans
• Air from lungs passes through edged to create vibrations when producing sounds
• Frequency of sounds relies on string tension
• Fundamental frequency averages 140 Hz for males and 230 Hz for females
• Vocal cord modifies sound as it travels through nasal area, along with tongue plays a role
• Voice that sounds are generate outside the vocal cords (for example, the consonant s)
• Artificial generated sounds that sound like animal sounds are used to lure creatures
• Electronic fish lures commercially exist, which mimics a mackerel distressed signal to lure larger fish

Medical Uses of Sound

• Baseline data on bats are used in studies
• Bechstein's bats call was produced lured into nets and released in one
• Mediterranean fruit fly/medfly causes $1B in damage, creating motivation for sound traps
• Male medfly vibrates wings at 350-Hz accompanied by complex harmonics
• The female medfly can detect this frequency to be lured into traps
• Stethoscopes used to analyze body with bell shape to flexible tube conduct sounds to the ear
• Modified stethoscope compares sounds from two body locations using a modified bell that evaluates both side of the human
• Helps listen to both and mother/fetus at the same time
• Ultrasound waves: waves by electrically driven millions of cycles per second, to high frequencies (very short wavelengths)
• Ultrasound waves can be focused and imaged like visible light to penetrate tissue
• Ultrasound creates images of absorption/reflection to examine structures on living thing
• Ultrasound usage safer than X-rays, providing similar information

Ultrasound Examination

• Ultrasonic methods can display motion of a fetus as well as the heart
• Doppler effect: frequency of detected sound depends on motion between source and observer
• f ′ = f × v / v±vs, where is the frequency and speed in the absence of motion, minus= approaching, and plus = moving
• Blood flowing ultrasonic measures are possible via measuring the change in frequency (Doppler effect) from scattered sound
• Mechanical energy transfers to heat inside tissue
• Diathermy, high energy ultrasound, heats patients bodies, a treatment relieving pain related to injuries
• High ultrasound energy destroys tissue, which removes kidney/gall stones (lithotripsy)