Sound is a form of energy produced by vibrating objects and propagated as longitudinal waves in a material medium through successive compressions and rarefactions.

Sound is called a mechanical wave because it requires a material medium (solid, liquid or gas) to travel; it cannot propagate through vacuum since particle interactions transmit the disturbance.

In a longitudinal wave, particles of the medium oscillate parallel to the direction of wave propagation; sound waves in air are a common example, showing compressions and rarefactions.

Wavelength (λ) is the distance between two successive compressions or rarefactions. Frequency (f) is the number of oscillations per second measured in hertz (Hz).

The wave relation is v = f × λ, where v is speed, f frequency and λ wavelength.

Amplitude is the maximum displacement of particles from their equilibrium. Larger amplitude means greater intensity and louder perceived sound; amplitude is related to energy transported by the wave.

Pitch refers to the perceived highness or lowness of a sound and is determined primarily by the frequency — higher frequency yields higher pitch.

Loudness is the subjective perception of sound strength by the ear and depends on intensity and frequency; intensity is the objective physical power per unit area (W·m⁻²) carried by the sound wave.

Frequency unit is hertz (Hz or s⁻¹). Intensity unit is watts per square metre (W·m⁻²).

The typical human hearing range is approximately from 20 Hz to 20,000 Hz (20 kHz), though it varies with age and individual differences.

Sound travels fastest in solids (particles closely packed), slower in liquids, and slowest in gases because transmission depends on elasticity and density of the medium.

A practical approximation is v ≈ 331 + 0.6 T m·s⁻¹, where T is temperature in °C; this shows speed increases with air temperature.

Higher temperature increases the average kinetic energy of molecules, allowing pressure disturbances to propagate faster, increasing the speed of sound.

Humid air contains water vapour which has lower molecular mass than dry air constituents — this reduces density and allows slightly faster propagation of sound, increasing speed marginally.

In ordinary conditions (non-dispersive medium like air for audible range), frequency does not significantly affect sound speed; all frequencies travel at nearly the same speed.

Obstacles can reflect, absorb or diffract sound waves. The amount of diffraction depends on the wavelength relative to obstacle size; low-frequency sounds diffract more and bend around obstacles.

An acoustic shadow is a region where sound intensity is significantly reduced behind an obstacle because the obstacle blocks or attenuates the wave.

Sound travels faster in water (≈1480 m·s⁻¹) and much faster in metals (e.g., steel ≈ 5000 m·s⁻¹) than in air (~340 m·s⁻¹).

Because the speed of sound in solids is much higher than in air, compressional disturbances reach the listener faster through solid media.

Reverberation time is the time taken for sound to decay to an inaudible level in an enclosed space due to multiple reflections; it affects speech clarity and acoustics of halls.

The angle of incidence equals the angle of reflection, measured with respect to the normal to the reflecting surface.

An echo is a reflected sound heard distinctly when the reflected sound reaches the listener after at least about 0.1 s delay compared to the original sound. For v ≈ 340 m·s⁻¹, one-way distance should be ≳17 m.

By measuring the time interval Δt between emission and reception of reflected sound; distance to reflector ≈ (v × Δt)/2 where v is speed of sound.

Echo is a distinct reflected sound heard after noticeable delay, while reverberation is the blending of many reflections arriving in quick succession giving prolonged sound.

Hard, smooth and large surfaces with little absorption (e.g., cliffs, concrete walls) reflect sound efficiently, producing clear echoes.

Absorbent materials reduce excessive reflections and reverberation, improving speech clarity and acoustic quality by damping unwanted echoes.

Sonar emits sound pulses and measures the time for echoes from underwater objects; using speed of sound in water, it calculates distance to objects (e.g., submarines, seafloor mapping).

For air at ~340 m·s⁻¹, minimum one-way distance ≈ 17 m (round-trip ~34 m) to produce a distinct echo after ~0.1 s.

Reflected sound leaves the surface such that the angle with respect to normal equals the incident angle, determining the direction of the reflected ray.

In lecture halls echoes are undesirable as they blur speech; adding sound-absorbing panels, curtains and carpets reduces reflections and improves intelligibility.

Beats are periodic variations in loudness due to interference of two close frequencies; beat frequency = |f₁ − f₂|, the absolute difference of frequencies.

Musicians listen to beats between a reference note and the instrument; minimizing beats (beat frequency → 0) indicates frequencies are matched and instrument is in tune.

The Doppler effect is the change in observed frequency when there is relative motion between source and observer; approaching increases apparent frequency, receding decreases it.

The change in pitch of a siren or car horn as the vehicle approaches and then moves away is an example of the Doppler effect.

Doppler effect changes the observed frequency, not the actual speed of sound in the medium. Measured speed from wave propagation remains determined by medium properties.

Constructive interference occurs when waves in phase add to increase amplitude (louder); destructive interference occurs when waves out of phase partially or fully cancel, reducing amplitude.

When two waves of nearly equal frequency interfere, alternating constructive and destructive interference occurs at beat frequency, producing periodic variations in loudness heard as beats.

Stationary (standing) waves occur when waves of equal frequency travel in opposite directions and superpose, producing nodes and antinodes; they are important in musical instruments (string and air column resonance).

Resonance occurs when a system is driven at its natural frequency leading to large amplitude oscillations; e.g., air column in an organ pipe resonates when driven by matching frequency, amplifying sound.

Timbre depends on the harmonic content (overtones) of a sound; different instruments produce different sets and relative strengths of harmonics even at the same fundamental frequency, giving unique tone quality.

Outer ear (pinna and ear canal), middle ear (tympanic membrane and ossicles — malleus, incus, stapes), and inner ear (cochlea and auditory nerve).

The tympanic membrane vibrates in response to incident sound waves and transmits these vibrations to the ossicles in the middle ear for amplification.

Different parts of the cochlea are tuned to different frequencies (tonotopic organization); hair cells at specific regions respond preferentially to certain frequencies converting mechanical motion into nerve impulses.

Threshold of hearing is the minimum sound intensity detectable by an average human ear, about 10⁻¹² W·m⁻² at 1 kHz.

Noise-induced hearing loss results from prolonged exposure to high-intensity sounds damaging hair cells; prevention includes using ear protection and reducing exposure duration and sound levels.

Ultrasonic waves have frequencies above 20 kHz (beyond human hearing). Applications include medical ultrasonography, ultrasonic cleaning, and nondestructive testing.

Infrasonic waves have frequencies below 20 Hz and are used in geophysics and monitoring natural phenomena like earthquakes and volcanic eruptions.

Ultrasound probes emit high-frequency pulses into the body; echoes from tissue interfaces are detected and timed to form real-time images of internal structures based on reflected intensities and time delays.

Earplugs reduce sound intensity reaching the ear, protecting delicate hair cells from damage and lowering the risk of noise-induced hearing loss.

Understanding sound helps in communication, music, medical diagnostics (ultrasound), engineering (noise control, sonar), and improves safety and quality of life through informed acoustic design.