Comprehensive Guide to Sound Physics and the Human Ear

Fundamentals of Sound and Vibration

• Sound waves are created whenever an object vibrates. A vibration is defined as a movement about a fixed point, often described as a to-and-fro or backwards and forwards movement.

• Common laboratory examples and instruments for producing sound via vibration include:   - A ruler: When held over the edge of a desk and 'twanged', its end moves up and down rapidly. A low whirring sound is heard, which becomes higher in pitch as the ruler is pulled further onto the desk (shortening the vibrating part).   - Elastic bands.   - Guitar strings.   - Tuning forks.

Production and Propagation of Sound Waves

• Sound waves require a medium to travel, such as a gas, a liquid, or a solid, because these states of matter contain particles.

• The process of sound travel involves the interaction between a vibrating object and surrounding particles:   - Compression: As a vibrating object moves towards nearby particles, it squashes them together. While the particles themselves are not compressed, the air pressure in that specific location rises because the particles are packed closer together.   - Rarefaction (Spread): As the object moves away from the nearby particles, it creates more space, allowing them to spread out. This causes the pressure at that location to fall.

• Propagation: As the object vibrates, the nearby air particles move backwards and forwards, causing adjacent particles further away to squash and spread in turn. This creates alternate regions of high and low pressure that travel through the air away from the source.

• Sound waves travel in all directions from the vibrating object.

Sound in Different Media

• Liquids: Sound travels very well through liquids. It moves faster and further in a liquid than it does in a gas because particles are held closer together by forces of attraction.   - Case Study: Humpback whales emit series of sounds called 'songs' that travel thousands of kilometres through the ocean for communication.

• Solids: Sound moves even faster through solids than through liquids due to the close interaction of particles. However, the sound does not typically travel as far as it does in liquids.   - Example: Snakes lack external ears but detect vibrations in the ground using their lower jaw bone. This bone transmits vibrations to the snake’s ears, allowing it to detect the footsteps of prey.

• Vacuum: Sound waves cannot pass through a vacuum because it lacks particles to transmit pressure variations.   - Experiment: A bell is placed in a sealed bell jar. As air is pumped out, the sound becomes quieter. Once a vacuum is established, the bell is silent even though the hammer can still be seen striking it.

Describing Sound Waves

• Sound waves can be represented on a displacement/distance graph.

• Key Wave Features:   - Amplitude: The height of the crest or the depth of the trough. It represents the maximum displacement of particles from their rest position ($‘rest’$ position refers to the initial location of a particle before the wave passes through).   - Wavelength: The distance from the top of one crest to the top of the next crest, or from the bottom of one trough to the bottom of the next trough.

• Particle Positions on a Waveform:   - Position X: The particle is moving through the rest position.   - Position Y: The particle has moved the maximum distance in one direction (at the peak of a crest).   - Position Z: The particle has moved the maximum distance in the opposite direction (at the bottom of a trough).

Human Hearing and the Ear

• The ear is the primary organ for detecting sound waves and is divided into three sections: the outer ear, the middle ear, and the inner ear.

• The Outer Ear:   - Sound waves are collected and passed down the auditory canal.   - Some waves are reflected into the canal by the outer part of the ear.   - At the end of the canal is the eardrum, a thin membrane that vibrates as sound waves push and pull on it.

• The Middle Ear:   - Contains three bones named for their shapes: the hammer, the anvil, and the stirrup.   - These bones are connected to increase the strength of the vibrations.

• The Inner Ear:   - The bones transmit vibrations to the oval window, which sets up vibrations in the ear fluid.   - Ear fluid vibrations travel into the cochlea, which contains a long row of tiny fibres.   - Each fibre is tuned to vibrate in response to a specific pitch.   - Vibrate fibres stimulate nerve endings, sending a nerve impulse (message) to the brain via the auditory nerve.

• The Eustachian tube connects the ear to the throat.

Measuring and Visualizing Sound

• Oscilloscopes allow for the visual display of sound waves.

• Cathode Ray Oscilloscope (CRO):   - Contains a cathode ray tube.   - Cathode rays create a spot on the screen that moves from left to right.   - When a microphone converts sound into electrical signals, the spot moves up and down, creating a visible waveform.

• Digital Oscilloscope:   - Newer technology that processes electrical signals from microphones using electrical circuits rather than cathode rays.   - Advantage: Can store displays in a data bank for future study and analysis.

Loudness and Intensity

• Loudness is directly related to the amplitude of the vibration.   - Small movement from rest = small amplitude = quiet sound.   - Large movement from rest = large amplitude = loud sound.

• Energy: Sound energy travels as particles move to and fro. High amplitude waves carry a large amount of energy, which is converted into movement energy (kinetic) in the eardrum and ear bones.

• Decibels ($dB$): The unit of measurement for sound loudness.   - $140\,dB$: The sound hurts/Pain threshold.   - $130\,dB$: Jet aircraft taking off.   - $110\,dB$: Road drill.   - $100\,dB$: Jet plane overhead.   - $90\,dB$: Noisy factory floor.   - $80\,dB$: Vacuum cleaner.   - $70\,dB$: Busy street.   - $60\,dB$: Busy department store.   - $55\,dB$: Normal speech.   - $40\,dB$: Voices in a town at night.   - $20\,dB$: A whisper.   - $10\,dB$: Rustling leaves.   - $0\,dB$: Limit of normal hearing.

Hearing Impairment and Protection

• Perforated Eardrum: Caused by the strong pushing/pulling force of very loud sounds (e.g., an explosion) which tears a hole in the membrane. It prevents efficient vibration but can heal over time.

• Nerve Deafness: Permanent damage caused by exposure to very loud sounds or specific notes for long periods. This happens when the vibrations in the ear fluid are so strong they damage the cochlea fibres. Pop musicians and industrial workers are at high risk.

• Ear Protection: Ear muffs are used by airport and factory workers to reduce the sound energy entering the ears.

• Ear Wax: A common cause of partial deafness in the outer ear which prevents waves from reaching the eardrum. It can be removed medically.

• Tissue Growth: Growths in the middle ear can stop ear bones from moving freely. Hearing aids (containing a microphone and amplifier) restore some of the amplification lost by the bones.

Pitch and Frequency

• Pitch refers to how high or low a sound is (e.g., 'bing' vs 'bong').

• Frequency: The number of sound waves produced per second as an object vibrates.   - Measured in hertz ($Hz$).   - Higher frequency results in a higher pitch and a shorter wavelength.

• Displacement/Time Graphs: Used to visualize sound waves over time.   - High-frequency sound: Waves are packed closer together.   - Low-frequency sound: Waves are spread further apart.

• Human Hearing Range: A young person typically hears frequencies between $20\,Hz$ and $20,000\,Hz$. The ability to detect high frequencies usually decreases with age.

Questions & Discussion

• Tuning Fork Demonstration: When a table tennis ball on a thread touches a vibrating tuning fork, it swings back and forth. This demonstrates that the fork is vibrating and that these vibrations are transferred as energy to move the ball, paralleling how the fork moves air particles to create waves.

• Bell Jar Vacuum: The bell cannot be heard in a vacuum because there are no particles to transmit the pressure changes of the sound wave. The hammer is visible because light can travel through a vacuum, unlike sound.

• Frequency Comparison: Between $1800\,Hz$, $50\,Hz$, and $10,000\,Hz$:   - Highest pitch: $10,000\,Hz$.   - Lowest pitch: $50\,Hz$.   - Hz stands for Hertz.

• Practical Advice: To prevent damage, listeners should keep headphone volumes moderate and avoid standing directly next to speakers at concerts or discos. Over time, high volumes can cause nerve deafness that prevents hearing specific ranges of notes.