Sound

Sound is a longitudinal wave — it's transmitted through the oscillation of particles in the same direction as the wave's propagation. As a mechanical wave, sound requires a deformable medium — air, water, or solid materials — to travel through. The oscillating particles compress and expand, creating alternating regions of high pressure (compressions) and low pressure (rarefactions) that carry the sound wave forward.

Key Takeaways

• Sound is a longitudinal mechanical wave requiring a medium; speed depends on the medium's bulk modulus and density: v = √(B/ρ).

• Pitch is our perception of frequency; human hearing spans 20 Hz–20,000 Hz, with infrasonic below and ultrasonic above that range.

• The Doppler effect shifts perceived frequency based on relative motion between source and observer: f′ = f(v ± v₀)/(v ∓ vₛ).

• A shock wave/sonic boom occurs when an object moves at or above the speed of sound.

• Intensity (I=P/A, in W/m²) is proportional to amplitude² and inversely proportional to distance²; the decibel scale (β=10log(I/I₀)) compresses the huge range of audible intensities logarithmically.

• Attenuation reduces amplitude/intensity/loudness over distance without changing frequency; beats arise from interfering waves of slightly different frequency, with f_beat = |f₁−f₂|.

• Standing waves in strings and open pipes support all harmonics (λ=2L/n); closed pipes support only odd harmonics (λ=4L/n).

• Ultrasound uses reflected high-frequency sound waves at tissue boundaries to build real-time medical images.

The Speed of Sound

The speed at which sound propagates through a medium depends on two properties: the bulk modulus (B) and the density (ρ) of the medium.

v = √(B/ρ)

The bulk modulus measures a medium's resistance to compression — how easily it can be deformed under pressure. The greater the bulk modulus, the faster sound travels through the material. Density, by contrast, refers to mass per unit volume; higher density tends to slow sound down, since particles are more tightly packed and harder to move. Together, these properties explain why sound travels fastest through solids, slower through liquids, and slowest through gases.

Pitch and the Range of Human Hearing

Sound is produced by the mechanical disturbance of particles along the wave's direction of propagation — for example, when a speaker vibrates, it causes air particles to oscillate, creating compressions and rarefactions that travel outward and are perceived by our ears as sound.

Our perception of a sound's frequency is called pitch. Lower-frequency waves produce lower-pitched sounds (like a bass guitar); higher-frequency waves produce higher-pitched sounds (like a violin). Human hearing generally ranges from 20 Hz to 20,000 Hz. Sound waves below 20 Hz are infrasonic — too low for humans to detect. Waves above 20,000 Hz are ultrasonic, with practical applications including medical imaging and sonar technology.

MCAT Callout — Pitch vs. Loudness: Pitch is our perception of a sound's frequency. Loudness is our perception of a sound's intensity. A sound can be high-pitched and quiet, or low-pitched and loud — the two are independent properties.

The Doppler Effect

Sound waves are also shaped by the motion of the source and the observer. The Doppler effect describes how a wave's perceived frequency changes when there is relative motion between the source and the observer.

When a source and observer move toward each other, perceived frequency increases, producing a higher-pitched sound. When they move apart, perceived frequency decreases, producing a lower-pitched sound — this is why a siren sounds higher-pitched as an ambulance approaches and lower-pitched as it drives away. Mathematically:

f′ = f(v ± v₀)/(v ∓ vₛ)

Here, f′ is the perceived frequency, f is the actual frequency of the source, v is the speed of sound in the medium, v₀ is the observer's speed, and vₛ is the source's speed. A positive sign is used when the observer and source move toward each other; a negative sign is used when they move apart.

Worked example. A source emits sound at 500 Hz. The speed of sound is 340 m/s. If the source moves toward a stationary observer at 20 m/s: f′ = f(v/(v − vₛ)) = 500(340/(340−20)) = 500(340/320) ≈ 531 Hz.

The observer perceives a higher frequency than the source actually emits, since the source is closing the distance between each successive wave crest.

This effect isn't limited to sound — it also applies to electromagnetic waves like light, causing redshift when objects move away from an observer and blueshift when they move closer.

Shock Waves and Sonic Booms

A shock wave forms when an object moves through a medium — such as air — at or above the speed of sound. The object compresses the air in front of it into a highly condensed wave front with a large pressure differential. This sudden pressure change is experienced as a sonic boom when the shock wave reaches an observer, because the compressed sound waves travel together in a single front, releasing energy in a burst rather than dispersing gradually.

Sound Intensity

How loud a sound appears relates directly to its intensity — the average rate of energy transfer per unit area across a surface perpendicular to the wave's direction of travel:

I = P/A

where I is intensity, P is the power carried by the wave, and A is the area over which the energy is spread. Intensity is measured in watts per square meter (W/m²). Louder sounds have higher intensities because more energy transfers per unit area.

Two relationships determine a sound wave's intensity:

• Intensity is proportional to the square of amplitude. If amplitude doubles, intensity increases by a factor of four.

• Intensity is inversely proportional to the square of distance from the source. As sound spreads out over a larger area moving away from the source, its energy becomes less concentrated — which is why sounds get quieter the farther you are from the source.

The Decibel Scale

Because the human ear can detect an enormous range of sound intensities, sound level is measured on the logarithmic decibel (dB) scale, which compresses that range into more manageable numbers:

β = 10log(I/I₀)

Here, β is the sound level in decibels, I is the intensity of the sound, and I₀ is the reference intensity — typically the threshold of human hearing, about 10⁻¹² W/m².

To find how sound level changes when intensity changes:

β_f − β_i = 10log(I_f/I_i)

where β_f and β_i are the final and initial sound levels, and I_f/I_i is the ratio of final to initial intensity.

Worked example. If a sound's intensity increases by a factor of 100 (I_f/I_i = 100), the change in sound level is: β_f − β_i = 10log(100) = 10(2) = 20 dB.

For reference: a whisper is around 20 dB, normal conversation around 60 dB, and a jet taking off at close range can reach around 140 dB — near the threshold of pain for the human ear (commonly cited in roughly the 120–140 dB range). Sound levels above 160 dB can cause instant damage, such as perforating the eardrum. This logarithmic scale highlights just how sensitive human hearing is — small changes in decibels represent large changes in intensity.

Attenuation and Beats

Sound waves don't maintain their original intensity indefinitely as they travel. This gradual loss of intensity is called attenuation, caused by damping effects like friction, air resistance, and viscous drag, which reduce amplitude, intensity, and perceived loudness over time. Importantly, attenuation affects only energy and amplitude — it does not alter frequency, so a sound may grow quieter without its pitch changing.

Sound waves can also exhibit periodic loudness variations due to interference. When two sound waves with slightly different frequencies interfere, they produce beats — a periodic fluctuation in loudness. The beat frequency is:

f_beat = |f₁ − f₂|

This reflects how often the volume rises and falls per second as the two waves move in and out of phase. Beats are commonly heard when two musical instruments are slightly out of tune with each other.

Standing Waves in Strings and Pipes

Standing waves form along objects with fixed boundaries at both ends — a string or an air column. Boundaries come in two types: a closed boundary, which doesn't allow oscillation and corresponds to a node (zero displacement), and an open boundary, which allows maximum oscillation and corresponds to an antinode (maximum displacement).

Strings fixed at both ends (like a guitar string) have closed boundaries — nodes — at both ends. The wavelength-length relationship is:

λ = 2L/n, n = 1, 2, 3, …

where n is the harmonic number, representing how many half-wavelengths fit along the string. The first harmonic (fundamental frequency, n=1) has the longest wavelength (λ=2L) and lowest frequency; higher harmonics correspond to shorter wavelengths and higher frequencies.

Open pipes (both ends open to the environment) have antinodes at both ends, and follow the same relationship as strings:

λ = 2L/n, n = 1, 2, 3, …

In the first harmonic, the pipe length equals half a wavelength (L=λ/2).

Closed pipes (one end closed/node, one end open/antinode) only support odd harmonics:

λ = 4L/n, n = 1, 3, 5, …

In the first harmonic, the pipe length equals one-quarter of the wavelength (L=λ/4).

Standing waves at a glance

	Boundaries	Wavelength-length relationship	Allowed harmonics	First harmonic
String (fixed both ends)	Node — Node	λ = 2L/n	All integers (n=1,2,3...)	L = λ/2
Open pipe (both ends open)	Antinode — Antinode	λ = 2L/n	All integers (n=1,2,3...)	L = λ/2
Closed pipe (one end closed)	Node — Antinode	λ = 4L/n	Odd integers only (n=1,3,5...)	L = λ/4

These harmonic patterns explain how musical instruments produce distinct pitches — each harmonic corresponds to a specific tone, and the combination of harmonics gives instruments their characteristic sound.

Ultrasound

Ultrasound applies high-frequency sound waves — well beyond human hearing — to create detailed images of internal organs, tissues, and structures. A handheld device called a transducer sends high-frequency waves into the body. As they travel through tissues of varying densities, some waves reflect back to the transducer at each tissue boundary, while the rest continue deeper into the body. By analyzing the time it takes for reflected waves to return and how much of the wave reflects, an ultrasound machine constructs a real-time image of internal structures — a non-invasive technique commonly used to visualize organs, monitor fetal development, and detect abnormalities.

Common MCAT Mistakes

• Assuming sound travels fastest through air. Sound speed depends on bulk modulus and density (v = √(B/ρ)); solids have the highest bulk modulus relative to density, so sound travels fastest through solids, then liquids, then slowest through gases like air.

• Confusing pitch with loudness. Pitch tracks frequency; loudness tracks intensity. A sound can shift in pitch without changing volume, or grow louder without changing pitch — they're independent properties governed by different formulas.

• Mixing up the Doppler sign convention. The ± and ∓ signs in f′ = f(v ± v₀)/(v ∓ vₛ) depend on whether source and observer are moving toward or apart — always check the direction of relative motion before assigning a sign, rather than defaulting to "approaching = plus" for both terms.

• Treating attenuation as a frequency change. Attenuation reduces amplitude and intensity as a wave travels, making it quieter — but it does not change frequency. A fading sound keeps the same pitch.

MCAT-Style Concept Check

Question: An open pipe and a closed pipe have the same length L. Comparing their first (fundamental) harmonics, which statement is correct?

• A) Both pipes have the same fundamental wavelength.

• B) The open pipe's fundamental wavelength is twice the closed pipe's.

• C) The closed pipe's fundamental wavelength is twice the open pipe's.

• D) Only the closed pipe can produce a fundamental harmonic.

Answer: C

Explanation: For an open pipe, the first harmonic has L = λ/2, so λ = 2L. For a closed pipe, the first harmonic has L = λ/4, so λ = 4L. Comparing the two: the closed pipe's fundamental wavelength (4L) is twice the open pipe's fundamental wavelength (2L) for the same length L.

FAQ

Why does sound travel faster through solids than through air?

Sound speed depends on v = √(B/ρ), where B is the bulk modulus (resistance to compression) and ρ is density. Solids have a much higher bulk modulus relative to their density than liquids or gases, so despite being denser than air, sound still travels fastest through solids, slower through liquids, and slowest through gases.

What's the difference between infrasonic and ultrasonic sound?

Both fall outside the range of human hearing (20 Hz–20,000 Hz). Infrasonic sound refers to frequencies below 20 Hz — too low for humans to perceive. Ultrasonic sound refers to frequencies above 20,000 Hz — too high for humans to perceive, but used in applications like medical ultrasound imaging and sonar.

Why does an ambulance siren change pitch as it passes you?

This is the Doppler effect. As the ambulance approaches, the sound waves reach you more frequently, raising the perceived frequency (higher pitch). As it moves away, the waves reach you less frequently, lowering the perceived frequency (lower pitch) — even though the siren itself never changes its actual frequency.

What determines which harmonics a pipe can produce?

It depends on the pipe's boundary conditions. Open pipes (both ends open, antinodes at both ends) and strings fixed at both ends (nodes at both ends) support all integer harmonics (λ=2L/n). Closed pipes (one closed end/node, one open end/antinode) support only odd harmonics (λ=4L/n), because the mismatched boundary conditions only accommodate odd multiples of a quarter-wavelength.