Human Ear: Sound Perception and Transmission

The Human Ear and Sound Waves

• The human ear can detect an extraordinary range of sound intensities, from a faint whisper to a clap of thunder 10 billion times as loud.
• The ear can distinguish frequencies from 20 to 20,000 Hz, allowing us to recognize familiar voices and appreciate the nuances of music.

Physical Properties of Sound Waves

• Sound is a pressure wave traveling in a medium, usually air, but also in liquids and solids.
• The audible range for humans is 20-20,000 cycles per second (Hertz).
• Our hearing is particularly well-suited to frequencies near 3,700 Hz, which corresponds to human speech.

Energy Transmission in Sound Waves

• Energy is carried by sound waves in the form of moving pressure differences.
• Molecules of the medium vibrate to transmit the energy, but do not travel the length of the medium with the energy.
• The energy is carried by the compression of the medium, which moves along the length of the medium with a constant speed, c.

Sound Wave Propagation

• Sound waves propagate through a medium, such as air, by pushing molecules together, creating a pocket of higher pressure between areas of lower pressure.
• Each atom vibrates sinusoidally with a velocity, v = v0 sin(ωt), where ν0 is the amplitude of the velocity of the atom and ω is its angular frequency.

Speed of Sound and Intensity

• The speed of sound in air is constant through an air mass of uniform temperature, approximately 350 m/s or 785 mph.
• The intensity of a sound wave depends on the amount of energy it carries and is related to loudness, measured by the work done by the pressure wave per unit time on a surface of area A.
• Intensity, I, is calculated as: I = P ν / A, where P is the instantaneous pressure, ν is the instantaneous velocity of the atoms, and A is the area affected by the sound wave.