Sound Wave Characteristics

Why This Matters

Sound waves are mechanical waves that transfer energy through a medium—and that's exactly where they connect to the bigger picture of energy conservation you're being tested on in AP Physics 1. When the CED mentions that mechanical energy can be "dissipated as thermal energy or sound," it's telling you that sound represents one way energy leaves a mechanical system. Understanding how sound waves carry energy through amplitude, intensity, and frequency relationships helps you explain where energy goes in collisions, friction scenarios, and oscillating systems.

You're also building foundational wave mechanics here that connects to interference, superposition, and standing waves—concepts that show up repeatedly in both qualitative and quantitative problems. Don't just memorize that "amplitude affects loudness"—know that amplitude squared is proportional to energy, and that's why sound intensity matters in energy dissipation problems. When an FRQ asks where kinetic energy went in an inelastic collision, sound is part of your answer.

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Fundamental Wave Properties

These three quantities—frequency, wavelength, and amplitude—define any wave mathematically. They're connected through the wave equation and determine everything from pitch to energy content.

Frequency

• Measured in Hertz (Hz)—the number of complete wave cycles passing a point per second
• Directly determines pitch; higher frequency means higher perceived pitch in sound
• Inversely related to wavelength through the wave equation $v = f\lambda$; if speed is constant, increasing frequency decreases wavelength

Wavelength

• The spatial period of a wave—distance from one crest to the next (or any point to the next identical point)
• Inversely proportional to frequency when wave speed is fixed; longer wavelengths mean lower frequencies
• Determines diffraction behavior; waves diffract more noticeably when wavelength is comparable to obstacle/opening size

Amplitude

• Maximum displacement from equilibrium position—how far particles move from their rest position as the wave passes
• Directly related to energy; wave energy is proportional to amplitude squared ($E \propto A^2$)
• Determines loudness in sound waves; greater amplitude means more energy delivered to your ear

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Energy and Power in Sound Waves

Sound waves transport energy without transporting matter. The rate of energy transfer and how it spreads through space determine what we actually hear.

Speed of Sound

• Approximately 343 m/s in air at room temperature—but varies significantly with medium and temperature
• Faster in denser, stiffer media; sound travels faster in solids than liquids, and faster in liquids than gases
• Calculated using $v = f\lambda$; knowing any two quantities lets you find the third

Intensity

• Power per unit area, measured in $\text{W/m}^2$—how much energy passes through a surface each second
• Proportional to amplitude squared ($I \propto A^2$); doubling amplitude quadruples intensity
• Decreases with distance from a point source following the inverse square law; this is why sounds get quieter as you move away

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Perception vs. Physics

These terms describe how humans experience sound, which differs from the objective physical quantities. Understanding this distinction helps you avoid confusing subjective perception with measurable physics.

Pitch

• The perceived frequency of a sound—higher frequencies sound "higher" to us
• Subjective and listener-dependent; hearing ability affects pitch perception, especially at frequency extremes
• Musical notes correspond to specific frequencies; A4 = 440 Hz is the standard tuning reference

Loudness

• Perceived intensity of sound—our subjective experience of how "loud" something is
• Measured in decibels (dB) on a logarithmic scale; every 10 dB increase represents 10× the intensity
• Frequency-dependent perception; human ears are most sensitive around 2000–5000 Hz, so sounds in this range seem louder at the same intensity

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Wave Behavior at Boundaries

When sound waves encounter obstacles, boundaries, or changes in medium, their behavior follows predictable rules. These phenomena explain everything from echoes to why you can hear around corners.

Reflection

• Sound bouncing off surfaces—follows the law of reflection where angle of incidence equals angle of reflection
• Creates echoes when reflected sound reaches the listener with sufficient delay (typically >0.1 seconds)
• Depends on surface properties; hard, smooth surfaces reflect well, while soft, irregular surfaces absorb sound

Refraction

• Bending of waves when speed changes—occurs when sound passes between media of different densities or temperatures
• Changes wave direction but not frequency; wavelength adjusts to accommodate the new speed
• Explains atmospheric effects; sound travels farther over water at night because temperature gradients bend waves downward

Diffraction

• Spreading of waves around obstacles or through openings—allows sound to reach areas not in direct line of sight
• More pronounced for longer wavelengths; low-frequency sounds (bass) diffract more than high-frequency sounds (treble)
• Wavelength-to-opening ratio matters; maximum diffraction occurs when wavelength is comparable to opening size

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Wave Superposition Phenomena

When multiple waves occupy the same space, they combine according to the superposition principle. The resulting patterns explain beats, noise cancellation, and musical instrument acoustics.

Interference

• Superposition of two or more waves creating a combined wave pattern
• Constructive interference occurs when waves align in phase, amplifying displacement; destructive interference occurs when waves are out of phase, reducing displacement
• Creates beats when two slightly different frequencies interfere, producing periodic loudness fluctuations at frequency $f_{beat} = |f_1 - f_2|$

Standing Waves

• Stationary wave patterns formed when identical waves travel in opposite directions and interfere
• Characterized by nodes and antinodes; nodes have zero displacement, antinodes have maximum displacement
• Fundamental to musical instruments; strings and air columns produce standing waves at specific resonant frequencies

Resonance

• Amplified oscillation at natural frequency—occurs when driving frequency matches an object's natural frequency
• Dramatically increases amplitude because energy transfers efficiently into the system
• Essential for instrument design; resonating cavities and bodies amplify specific frequencies to produce louder, richer sound

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Relative Motion Effects

When sources or observers move, the perceived wave properties change in predictable ways. This connects wave mechanics to kinematics and relative motion.

Doppler Effect

• Apparent frequency shift due to relative motion—approaching sources have higher perceived frequency, receding sources have lower
• The source doesn't actually change frequency; the relative motion compresses or stretches the wavelengths reaching the observer
• Quantified by Doppler equations; the shift depends on the speeds of source and observer relative to the wave speed in the medium

Harmonics

• Integer multiples of the fundamental frequency—the fundamental (first harmonic) is $f_1$, second harmonic is $2f_1$, and so on
• Determine timbre (tone quality); different instruments playing the same note have different harmonic content
• Produced naturally in standing wave systems; strings and air columns support multiple harmonic frequencies simultaneously

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Quick Reference Table

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Self-Check Questions

1. A wave's amplitude doubles. By what factor does its intensity change, and how does this relate to energy dissipation in an inelastic collision?

2. Which two wave behaviors—reflection, refraction, or diffraction—both involve waves encountering boundaries, and what distinguishes them?

3. Compare standing waves and traveling waves: what must be true about two waves for a standing wave pattern to form, and where does energy accumulate in the pattern?

4. An ambulance approaches you, passes, and moves away. Describe how the perceived frequency changes and explain why the actual frequency emitted by the siren remains constant throughout.

5. If an FRQ states that kinetic energy is lost in a collision and asks where the energy went, how would you explain the role of sound using the concepts of amplitude and intensity?