Sound Properties: Amplitude, Period, Frequency, Wavelength

Higher frequency corresponds to higher pitch perception. Larger amplitude corresponds to louder sounds because amplitude measures the amount of air pressure perturbation, which directly relates to the energy transferred and perceived loudness. This establishes the fundamental relationship between physical wave properties and human auditory perception.

Sound wave properties determine perception: Frequency determines pitch—the shorter the wavelength, the higher the pitch. Amplitude determines loudness—the distance from peak/trough to equilibrium measures wave strength. Place theory explains that different hair cells along the cochlea respond to different frequencies, with base detecting high pitches and apex detecting low pitches.

The frequency of a sound wave directly corresponds to its pitch - a high-frequency sound has a high pitch because air molecules oscillate more rapidly back and forth. The amplitude of a sound wave corresponds to its intensity or loudness - increasing amplitude results in larger oscillations of air molecules, which the ear perceives as a louder sound. This relationship between physical wave properties and human perception explains why we hear different qualities from the same instrument played at different volumes or with different playing techniques.

Pitch is determined by frequency (振動数) - higher frequency means higher pitch. Loudness is determined by the amplitude of the pressure wave - larger amplitude means louder sound. The ear membrane vibrates more for louder sounds, which is why extremely loud sounds can damage hearing.

Amplitude is maximum particle displacement from mean position, determining sound loudness—greater amplitude means louder sound. Wavelength is distance between consecutive points in phase. Loudness and pitch are independent properties: loudness depends on amplitude while pitch depends on frequency. Higher frequency means higher pitch. Men's voices typically have lower pitch than women's due to longer vocal cords vibrating more slowly. Frequency measures vibrations per second (unit: hertz, Hz), while time period measures seconds per vibration (reciprocals: T = 1/f). These properties explain how we perceive and differentiate various sounds.

Reflection occurs when waves encounter boundaries they cannot pass through, with angle of incidence equal to angle of reflection. Refraction occurs when waves pass between media and change direction due to speed changes, described by Snell's Law: n1 sin(θ1) = n2 sin(θ2), where n = c/v. When waves travel from denser to less dense media at angles greater than the critical angle, total internal reflection occurs. Interference occurs when two waves meet: constructive interference (in-phase) produces greater amplitude when path difference is integer multiple of wavelength (Δd = nλ), while destructive interference (out-of-phase) produces reduced amplitude when path difference is odd multiple of half-wavelength (Δd = (n + 1/2)λ).

Four fundamental wave phenomena govern wave behavior: reflection (bouncing back), refraction (bending due to medium changes), diffraction (spreading around obstacles/gaps), and interference (superposition of overlapping waves). Reflection is used in sonar for depth measurement. Refraction and diffraction together explain coastal geography - bays are calmer than capes due to diffraction patterns. Diffraction causes waves to spread wider through gaps. Interference requires coherent sources; for light, additionally requires monochromatic light. Constructive interference occurs when crests meet crests or troughs meet troughs, producing resultant amplitudes of +2A or -2A (stronger waves). Destructive interference occurs when crests meet troughs, producing zero amplitude (weaker waves). Detection methods vary: sound interference shows louder/softer sounds; light interference shows bright/dark fringes.

Four fundamental wave phenomena: (1) Reflection - angle of incidence equals angle of reflection; fixed end causes inversion, free end does not; (2) Refraction - wave bends when changing media; frequency constant, speed and wavelength change; Snell's Law: sin(θ₁)/sin(θ₂) = v₁/v₂; critical angle produces 90° refraction; (3) Diffraction - waves bend around obstacles; Huygens' Principle states every point on wavefront acts as new source; significant when obstacle size ≤ wavelength; (4) Interference - coherent sources produce constructive (path diff = nλ) and destructive (path diff = (n-1/2)λ) interference patterns.

Waves exhibit four fundamental behaviors: interference (constructive combines waves to increase amplitude when crests overlap, while destructive reduces amplitude when crests meet troughs); diffraction (waves spread around obstacles or through openings, with smaller gaps producing greater spreading); reflection (waves bounce off surfaces following the law that angle of incidence equals angle of reflection); and refraction (waves bend when traveling into a new medium with different properties).

The Doppler effect describes the perceived change in frequency when there is relative motion between a wave source and an observer. Frequency is the number of complete waves passing a point per second. When the source and observer move toward each other, waves appear compressed, increasing the observed frequency. When moving away, waves spread apart, decreasing the observed frequency. The speed of sound remains constant (~330 m/s), so frequency and wavelength change inversely. Importantly, this is a perceived change—the actual emitted frequency remains unchanged; only our perception of it changes based on relative motion.

The Doppler effect describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. When the source and observer are moving toward each other, the observed frequency increases. When they are moving away from each other, the observed frequency decreases. This change in frequency is called the apparent frequency, which differs from the actual frequency of the source.

The Doppler effect describes how the perceived frequency of sound changes based on the relative motion between the sound source and the observer. When a sound source moves toward an observer, the frequency appears higher, and when it moves away, the frequency appears lower. The actual frequency of the source remains constant.

The Doppler effect describes how observed frequency changes when there is relative motion between sound source and observer. When the observer moves toward a stationary source, observed frequency increases: f' = f(1 + v/v_sound). When the source moves toward a stationary observer, observed frequency increases: f' = f(v_sound/(v_sound - v)). When both move, f' = f(v_sound ± v_observer)/(v_sound ∓ v_source). The effect occurs because relative motion changes the number of wave crests encountered per unit time.

The Doppler effect describes how observed sound frequency changes with relative motion between source and observer. When a source moves toward a stationary observer, observed frequency increases because successive wave crests arrive more frequently. When moving away, observed frequency decreases. This occurs because changing distances compress or stretch sound waves. The phenomenon distinguishes actual frequency (source-generated) from apparent frequency (observer-perceived). The mathematical framework relates these quantities through wave mechanics, showing that relative motion fundamentally alters perception of sound characteristics.

Power (P) is energy transfer rate in watts. Intensity (I) is power per unit area (W/m²), calculated as I = P/(4πr²) for spherical spreading. The decibel scale measures intensity logarithmically: β = 10 × log₁₀(I/I₀), where I₀ = 10⁻¹² W/m² is the hearing threshold. This logarithmic scale compresses the enormous range of intensities (from 10⁻¹² to 10² W/m²) that human ears can detect into manageable numbers.

Wave intensity is the average energy flowing through a unit area perpendicular to wave propagation per unit time: I = P/A, where P is power and A is cross-sectional area. Intensity is proportional to the square of amplitude (I ∝ A²) and the square of frequency (I ∝ f²). The decibel scale measures sound intensity levels logarithmically: dB = 10 × log₁₀(I/I₀), where I₀ is the reference intensity (10⁻¹² W/m²). An increase of 10 dB corresponds to a tenfold increase in intensity, while a 3 dB increase corresponds to approximately doubling the intensity.

Power equals the square of amplitude, representing acoustic energy. Intensity is power relative to a reference sound, typically the quietest sound human ears can hear. The decibel (dB) scale uses logarithms to compress the enormous range of human hearing into manageable numbers. One bel equals log₁₀(power_x/power_ref), and one decibel equals 0.1 bel. A logarithm to base 10 answers: How many times must 10 be multiplied by itself to obtain a given number? For example, log₁₀(10) = 1, log₁₀(100) = 2, log₁₀(1000) = 3. This logarithmic relationship enables practical expression of sounds ranging from whisper-quiet to painfully loud on a single scale.

Sound intensity is power per unit area (I = P/A). The intensity formula for sound waves is I = (Δp)²/(2ρωv), where Δp is pressure amplitude, ρ is density, and v is speed of sound. The decibel scale uses β = 10 log₁₀(I/I₀), with I₀ = 10⁻¹² W/m² as the hearing threshold. This logarithmic scale compresses the 16-order-of-magnitude range of human hearing. Logarithm properties: log(x) + log(y) = log(xy), log(x) - log(y) = log(x/y), log(xⁿ) = n log(x). Doubling intensity increases decibels by 3 dB.

Sound intensity is the power per unit area carried by a sound wave, measured in watts per square meter. The decibel scale is a logarithmic scale used to express sound intensity levels. The relationship between sound intensity level (in decibels) and intensity is given by β = 10 × log₁₀(I/I₀), where I₀ is the reference intensity (typically 10⁻¹² W/m²). This logarithmic scale allows us to express the vast range of sound intensities that humans can hear in a manageable numerical range.