Key Sound Wave Properties

Why This Matters

Sound wave properties form the foundation of everything you'll encounter in acoustics—from understanding why concert halls sound different from your bedroom to explaining how noise-canceling headphones work. You're being tested on your ability to connect measurable wave characteristics like frequency, amplitude, and wavelength to real-world phenomena like pitch perception, loudness, and sound propagation. These concepts don't exist in isolation; they interact constantly, and exam questions will expect you to trace those connections.

Don't just memorize that frequency is measured in Hertz or that amplitude relates to loudness. Know why these relationships exist and how changing one property affects others. When you see a question about sound behavior in different environments, you should immediately think about which wave properties are at play. Master the underlying physics, and the applications—from sonar to architectural design—will make intuitive sense.

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Fundamental Wave Characteristics

These are the core measurable properties that define any sound wave. Every acoustic phenomenon you study traces back to these basic parameters and how they interact with each other and the environment.

Frequency

• Frequency measures wave cycles per second in Hertz (Hz)—it's the physical property that determines what we perceive as pitch
• Human hearing spans 20 Hz to 20,000 Hz, with peak sensitivity typically between 2,000–5,000 Hz where speech consonants fall
• Higher frequency means shorter wavelength—this inverse relationship ($f = v/\lambda$) is fundamental to understanding wave behavior

Wavelength

• Wavelength is the physical distance between successive wave crests—measured in meters, it determines how sound interacts with objects and spaces
• Inversely proportional to frequency through the relationship $\lambda = v/f$, where $v$ is the speed of sound
• Wavelength relative to object size determines acoustic behavior—sounds diffract around obstacles smaller than their wavelength but reflect off larger ones

Amplitude

• Amplitude is maximum particle displacement from equilibrium—the greater the displacement, the more energy the wave carries
• Directly correlates to perceived loudness, though human perception is logarithmic rather than linear
• Measured in decibels (dB) using the formula $L = 10 \log_{10}(I/I_0)$, where $I_0$ is the threshold of hearing

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Energy and Propagation

These properties describe how sound energy travels through space and different media. The key principle here is that sound requires a medium and its behavior depends entirely on that medium's properties.

Speed of Sound

• Approximately 343 m/s in air at 20°C—this baseline value appears constantly in calculations and problem sets
• Increases with medium density and temperature—sound travels ~1,480 m/s in water and ~5,000 m/s in steel
• Temperature dependence follows $v \approx 331 + 0.6T$ m/s in air, where $T$ is temperature in Celsius

Intensity

• Power per unit area, measured in W/m²—quantifies how much acoustic energy passes through a given surface
• Follows the inverse square law: $I \propto 1/r^2$, meaning intensity drops to one-quarter when distance doubles
• Related to amplitude squared ($I \propto A^2$)—doubling amplitude quadruples intensity, a crucial relationship for calculations

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Wave Interactions

When sound waves encounter boundaries, obstacles, or other waves, these behaviors emerge. Understanding these interactions is essential for architectural acoustics, audio engineering, and environmental sound modeling.

Reflection

• Sound bounces off surfaces following the law of reflection—angle of incidence equals angle of reflection
• Creates echoes when delay exceeds ~50 ms and reverberation when multiple reflections blend together
• Hard, smooth surfaces reflect efficiently; soft, porous materials absorb sound energy instead

Refraction

• Sound bends when passing between media with different speeds—governed by Snell's Law: $\sin\theta_1/v_1 = \sin\theta_2/v_2$
• Temperature gradients cause refraction in air—sound bends toward cooler air, explaining why sound carries farther at night
• Critical for understanding long-distance sound propagation in outdoor environments and underwater acoustics

Diffraction

• Sound spreads around obstacles and through openings—this is why you can hear around corners
• Most pronounced when wavelength is comparable to or larger than the obstacle—low frequencies diffract more than high frequencies
• Explains why bass travels through walls while treble is blocked, and why outdoor sound reaches shadowed areas

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Wave Superposition

When multiple waves occupy the same space, they combine according to the superposition principle. Phase relationships determine whether waves reinforce or cancel each other.

Phase

• Describes a wave's position in its cycle—measured in degrees (0°–360°) or radians (0–$2\pi$)
• In-phase waves (0° difference) add constructively; out-of-phase waves (180° difference) cancel destructively
• Critical for microphone placement and speaker arrays—small position changes create significant phase shifts

Interference

• Occurs when two or more waves overlap in space—the resulting amplitude equals the sum of individual wave displacements
• Constructive interference doubles amplitude (and quadruples intensity); destructive interference can produce silence
• Basis for noise-canceling technology—generating anti-phase waves to cancel unwanted sound

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Quick Reference Table

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Self-Check Questions

1. If you double the frequency of a sound wave while the speed of sound remains constant, what happens to the wavelength? What acoustic consequence does this have for diffraction behavior?

2. Which two properties both affect perceived loudness, and how are they mathematically related to each other?

3. Compare and contrast reflection and refraction: both change sound direction, but what fundamentally different conditions cause each phenomenon?

4. A concert hall designer wants to prevent "dead spots" where audience members hear diminished sound. Which wave property is primarily responsible for dead spots, and what causes them?

5. Why does sound travel faster in water than in air, yet faster in steel than in water? Explain the relationship between medium properties and speed of sound that accounts for this pattern.