Chapter 1 Exercises: What Is Sound?

Waves, Pressure, and the Physics of Hearing

These exercises progress from factual recall through conceptual understanding, analysis, synthesis, and finally research extension. Work through them in order, or jump to the level that challenges you.

Part A: Factual Recall

These questions test your command of definitions, units, and basic relationships from the chapter. All answers can be found directly in the text.

A1. Define the following terms in your own words (one sentence each): - Mechanical wave - Longitudinal wave - Amplitude - Frequency - Wavelength

A2. State the wave equation relating speed, frequency, and wavelength. Using it, calculate the wavelength of each of the following sounds in air at 20°C (speed of sound = 343 m/s): - A 20 Hz infrasound wave (lowest limit of human hearing) - A 1,000 Hz tone (middle of the audible range) - A 15,000 Hz tone (high treble, near upper limit for many adults) - A 40 Hz bass guitar note

A3. Fill in the blanks: Sound in air is a _ wave, meaning the medium oscillates _ to the direction of wave travel (parallel / perpendicular). By contrast, waves on a stretched string are _ waves. This distinction means that the familiar sine-wave diagram of sound is actually a _ (literal picture / graph of pressure over time).

A4. List the three bones of the middle ear (ossicles) and describe the functional problem they solve. What is the name of the phenomenon that would occur if the eardrum were connected directly to the cochlear fluid without the ossicles?

A5. The threshold of human hearing corresponds to a sound pressure of 20 micropascals. A normal conversation occurs at approximately 60 dB SPL. Using the decibel formula L = 20 × log₁₀(P/P₀), verify that 60 dB corresponds to a pressure 1,000 times larger than the threshold pressure. Show your calculation step by step.

Part B: Conceptual Application

These questions ask you to apply principles from the chapter to new situations. Think through the physics before writing.

B1. A singer standing in a large concert hall produces a note at 400 Hz. At the same moment, a member of the audience 30 meters away hears the note. - How long did the sound take to travel from singer to audience? (Use 343 m/s.) - Does the sound that arrives at 30 meters have a different frequency than what the singer produced? Does it have a different wavelength? Explain your reasoning. - If the temperature in the hall drops from 22°C to 15°C during the concert, does the speed of sound increase or decrease? By approximately how much? (Use the approximation: c ≈ 331 + 0.6T m/s.) What effect might this have on the acoustic experience?

B2. Two speakers in a recording studio produce the same 500 Hz tone at the same amplitude. If you stand at a point in the room where the distance from speaker A is exactly 0.34 meters longer than the distance from speaker B, what do you expect to hear, and why? (Hint: calculate the wavelength of 500 Hz and compare to 0.34 m.) What would happen if the distance difference were 0.686 m?

B3. A musician plays a note on a trumpet underwater (this has been done experimentally). - Does the note's frequency change underwater compared to in air? - Does the wavelength change? If so, by how much? (Sound speed in water: ~1,480 m/s) - The musician's embouchure (lip shape and tension) determines the vibration frequency. Would the acoustic behavior of the instrument change significantly underwater? Why?

B4. The inverse square law states that sound intensity decreases with the square of distance from a point source. A musician at a distance of 1 meter produces a sound of 90 dB. Using the inverse square law for intensity (and remembering that decibels scale with the logarithm of intensity), estimate the sound level at: - 2 meters away - 10 meters away - 100 meters away Note: For intensity I, I ∝ 1/r². Since L = 10 log₁₀(I/I₀), doubling the distance (r → 2r) means I drops by a factor of 4, which is a change of 10 log₁₀(4) ≈ 6 dB.

B5. You record your voice on a smartphone and play it back, finding that you sound noticeably different than you expected. Explain this observation using the concept of bone conduction. Which frequency components of your voice are most likely to be affected? What is the relationship between bone conduction and the physics of impedance?

Part C: Analysis

These questions ask you to compare, contrast, explain mechanisms, or reason about diagrams. Go beyond stating facts to explaining relationships.

C1. Compare and contrast the following pairs, explaining both the similarities and the key differences: - A) Infrasound and ultrasound (how are they physically the same as audible sound? How and why do human responses differ?) - B) Amplitude and loudness (why are these related but not identical?) - C) Frequency and pitch (same question — related, but not identical. What additional factors affect pitch perception?)

C2. Analyze the tonotopic organization of the basilar membrane. The membrane is narrow and stiff at the base and wide and floppy at the apex. Using your knowledge of resonance (think of a guitar string: how does stiffness and length affect frequency?), explain in physical terms why the base responds to high frequencies and the apex to low frequencies. What does this architecture accomplish that a uniformly stiff membrane could not?

C3. Consider the following scenario: two concert halls have the same volume (same interior space), but Hall A has hard, reflective walls (stone and plaster) while Hall B has soft, absorptive walls (heavy drapes, acoustic foam, carpeting). Analyze how the reverberation time would differ between the two halls. Which hall would be better suited for a Beethoven symphony? Which for an amplified rock concert? For a lecture? Justify each choice with acoustic reasoning.

C4. The decibel scale is logarithmic. A choir director wants to add more sopranos to make the choir louder. The choir currently has 16 sopranos, each producing approximately equal sound levels. - How many additional sopranos would need to be added to increase the total level by 3 dB (approximately)? - How many to increase by 6 dB? - By 10 dB? What does this analysis tell us about the practical limits of increasing volume by adding more voices?

C5. The chapter distinguishes between "noise" (aperiodic) and "music" (periodic/quasi-periodic) on physical grounds, but then complicates this distinction. Analyze three specific musical examples — one clearly periodic (sustained tone), one clearly aperiodic (struck snare drum), and one that blurs the boundary (your choice). For each, describe the physical nature of the sound and the cultural/musical context in which it functions. What does this analysis reveal about the relationship between physical description and musical meaning?

Part D: Synthesis

These questions ask you to combine concepts, design experiments, or create original applications of the chapter's ideas. There is no single correct answer.

D1. Design an experiment (no specialized equipment required — household items only) that would allow you to demonstrate three of the following concepts from this chapter to a group of 10-year-old students: - The longitudinal nature of sound waves - The relationship between frequency and pitch - The inverse square law (sound gets quieter with distance) - The difference between air conduction and bone conduction - The logarithmic nature of loudness perception

For each demonstration you choose, describe: what materials you need, the procedure, what the students should observe, and how you would explain the physics.

D2. The human hearing range spans roughly 20 Hz to 20,000 Hz — a ratio of 1,000:1. The visible light spectrum spans roughly 400 nm to 700 nm in wavelength, a ratio of about 1.75:1. If human hearing were compressed to the same proportional range as human vision, what frequencies could we hear? What would be lost? Conversely, if human vision were expanded to the same proportional range as hearing, what colors could we see? Reflect on what this comparison reveals about the design trade-offs of sensory systems.

D3. Imagine you are tasked with designing a music performance space specifically for submarine crew members to use during long deployments. The space is a cylindrical room 8 meters long and 4 meters in diameter, constructed of steel. Identify and explain at least four acoustic challenges that arise specifically because of the environment (the material, the geometry, the confined space), and propose one design solution for each. Apply the physical principles of this chapter in your reasoning.

D4. The chapter introduces the comparison between a choir and a particle accelerator as wave-interference systems. Identify two additional phenomena from everyday life (not from particle physics, not from music) that also involve the emergence of organized patterns from the superposition of many small, slightly different wave sources. For each phenomenon: describe what the "sources" are, what the "wave" is, and what "organized pattern" emerges. Explain why the collective result is different from what any single source would produce.

D5. Write a short (300–400 word) dialogue between a physicist and a musician arguing about whether music can be "fully explained" by physics. The physicist argues reductionism; the musician argues for emergence and cultural irreducibility. Make both characters argue thoughtfully, with reference to specific physical concepts from this chapter. Your dialogue should not have a "winner" — both positions should be left with genuine force at the end.

Part E: Research and Extension

These questions ask you to go beyond the chapter — look things up, explore primary sources, make connections to the world outside this book. They are designed to be open-ended.

E1. The chapter mentions that the reverberation time (RT60) of a Gothic cathedral can be 7–10 seconds. Research the specific case of a notable Gothic cathedral (Notre-Dame de Paris, Canterbury Cathedral, or one of your choosing). Find its approximate dimensions and reverberation time. Then research an example of medieval plainchant or Renaissance polyphony composed specifically for performance in such a space. What compositional techniques does the music use that make sense physically in the context of very long reverberation? (For instance: do phrases overlap? Are text syllables short or long? How fast is the tempo?)

E2. Infrasound — sound below 20 Hz — is produced by a variety of natural and human-made sources. Research at least three: one geological (earthquakes, volcanoes, avalanches), one meteorological (storms, tornadoes), and one animal (elephant rumbles, whale calls, tiger vocalizations). For each: what frequency range does the infrasound occupy? Over what distance does it travel effectively? What physical mechanism produces it? And what is known about whether humans (consciously or unconsciously) respond to infrasound in ways that might be relevant to musical experience in large spaces with powerful subwoofer bass?

E3. The audiogram is a clinical measurement of a person's hearing threshold at multiple frequencies, typically from 250 Hz to 8,000 Hz. Obtain or create a hypothetical audiogram for: (a) a typical healthy young adult (20 years old), (b) a typical adult with age-related hearing loss (65 years old), and (c) a musician with documented noise-induced hearing loss in the high-frequency range. For each audiogram, analyze which aspects of music listening would be most affected. Research whether and how musicians with significant hearing loss continue to compose and perform.

E4. The Haas effect (precedence effect) — the perceptual fusion of sounds arriving within approximately 30–50 ms of each other — is actively exploited in live concert sound reinforcement. Research how large-venue sound engineers use delayed speaker arrays (fill speakers, delay towers) to extend sound coverage without creating perceived echoes. What is the technical term for this technique? Find a specific example of a major concert venue or touring production that explicitly uses delay alignment based on the Haas effect. Describe the engineering involved.

E5. The bone conduction hearing pathway has been exploited in a variety of assistive hearing technologies beyond simple headphones. Research cochlear implants and bone-anchored hearing aids (BAHA). For each technology: what is the physical mechanism by which sound reaches the cochlea? Which patients benefit most from each technology, and why? What are the current engineering challenges and frontiers in each? As a synthesis: does the existence of these technologies support or complicate the philosophical position that "hearing is just physics"? Explain your reasoning.