5.1 Sound: Production, Intensity & the Doppler Effect

Sound: Production, Intensity & the Doppler Effect

Content Category 4D covers how mechanical (sound) and electromagnetic (light) waves are produced, how they travel, and how the body senses and uses them — hearing, ultrasound imaging, and the eye's optics all trace back to the physics in this chapter. This section starts with sound.

Production and Propagation of Sound

Sound is a longitudinal wave — unlike the transverse waves you saw with strings and light, the particles of the medium oscillate parallel to the direction the wave travels. A vibrating source (a guitar string, vocal cords, a tuning fork) pushes on adjacent molecules of the surrounding medium, creating alternating regions of compression (molecules squeezed together, higher pressure) and rarefaction (molecules spread apart, lower pressure) that propagate outward. Because sound is a pressure disturbance carried by matter, it cannot travel through a vacuum — there is no medium to compress and rarefy. This is a classic MCAT distinction from light, which is an electromagnetic wave that travels fastest through vacuum.

Speed of Sound in Different Media

The speed of a mechanical wave through a medium is set by two competing properties:

v = √(elastic modulus / ρ)

A stiffer medium (higher elastic/bulk modulus) transmits a pressure disturbance faster, because the molecules snap back into place — and push their neighbors — more quickly. A denser medium (higher ρ) slows the wave down, because more mass must be accelerated by the same restoring force. In practice, stiffness wins: going from gas to liquid to solid, stiffness increases far more than density does, so sound speed increases in that order:

This ordering — solids fastest, liquids next, gases slowest — is a high-yield MCAT fact. It also explains why you can hear an approaching train through the rails before you hear it through the air, and why ultrasound imaging (below) works better through soft tissue and fluid-filled structures than through air-filled lungs or bone interfaces, which scatter and distort the beam.

Frequency Range of Hearing and Wave Relations

Human hearing typically spans about 20 Hz to 20,000 Hz (20 kHz). Sounds below 20 Hz are infrasound; sounds above 20 kHz are ultrasound. Frequency (f), wavelength (λ), and wave speed (v) are always linked by the universal wave relation:

v = fλ

For a fixed medium (fixed v), higher frequency means shorter wavelength. A 343 Hz tone in air (v ≈ 343 m/s) has λ ≈ 1 m; a 3,430 Hz tone has λ ≈ 0.1 m. This inverse relationship reappears in ultrasound imaging, where higher probe frequencies produce shorter wavelengths and therefore finer spatial resolution.

Intensity and the Decibel Scale

Intensity (I) is the average power delivered per unit area perpendicular to the wave's direction of travel:

I = P / A

with SI units of W/m². For a point source radiating uniformly into a sphere of radius r, A = 4πr², so intensity falls as 1/r² (the inverse-square law). Doubling your distance from a point source cuts the intensity to one-quarter — roughly a 6 dB drop on the decibel scale defined below.

Human ears can detect an enormous range of intensities — roughly twelve orders of magnitude — so loudness is reported on a compressed logarithmic decibel (dB) scale instead of a linear one:

β (dB) = 10 log₁₀(I / I0)

where I0 = 1 × 10⁻¹² W/m² is the reference intensity, defined as the threshold of human hearing at 1,000 Hz. Because the scale is logarithmic:

• A 10-fold increase in intensity raises the decibel level by exactly 10 dB (since log₁₀10 = 1).
• A 100-fold increase in intensity raises the level by 20 dB (log₁₀100 = 2).
• Doubling the intensity raises the level by only about 3 dB (log₁₀2 ≈ 0.3), which is why a sound that is "twice as intense" often sounds only subtly louder to the ear.

Loudness is the subjective perception of intensity; it is roughly logarithmic in intensity but also depends on frequency (the ear is most sensitive near 1–4 kHz). On the MCAT, treat intensity (physics) and loudness (perception) as related but not identical quantities.

Attenuation (Damping)

As a sound wave travels, some of its energy is continuously absorbed by the medium and converted to heat, or scattered by inhomogeneities — this energy loss is attenuation, also called damping. Attenuation increases with both distance traveled and frequency: higher-frequency waves lose energy faster per unit distance than lower-frequency waves in the same medium. This trade-off is central to medical ultrasound: higher-frequency probes give sharper resolution but penetrate less deeply before the signal attenuates too much to be useful, while lower-frequency probes reach deeper structures at the cost of image detail.

The Doppler Effect

The Doppler Effect is the apparent shift in frequency (and wavelength) of a wave caused by relative motion between the source and the observer. The general relationship is:

f' = f × (v ± v0) / (v ∓ vs)

where f is the source's true (emitted) frequency, f' is the frequency the observer perceives, v is the speed of sound in the medium, v0 is the observer's speed, and vs is the source's speed. The sign convention always follows the same logic: use the sign that makes the frequency shift higher when source and observer are approaching each other, and lower when they are receding.

• Moving source, stationary observer: as the source moves toward the observer, it "crowds" successive wavefronts into a smaller space ahead of it, shortening the wavelength and raising the observed frequency (denominator decreases: v − vs). Moving away stretches the wavelength and lowers the frequency (v + vs).
• Moving observer, stationary source: an observer moving toward the source intercepts wavefronts more often, raising the perceived frequency (numerator increases: v + v0). Moving away lowers it (v − v0).
• Reflection from a moving object: when sound reflects off a moving object (a heart valve, a red blood cell, a car), the shift happens twice — once as the object "receives" the wave as a moving observer, and again as it "re-emits" the reflected wave as a moving source. This double-shift principle is exactly how Doppler echocardiography measures blood flow velocity and direction inside the heart and vessels.

Pitch is the subjective, perceptual correlate of frequency — a physics concept (frequency) translated into a psychoacoustic one (how "high" or "low" a tone sounds). Higher frequency is perceived as higher pitch.

Resonance in Pipes and Strings

A string fixed at both ends, or an air column open at both ends, must have a displacement node (string) or pressure antinode at each open/free boundary and supports standing waves at all integer harmonics:

λn = 2L / n, fn = nv / 2L (n = 1, 2, 3, …)

A pipe closed at one end (open at the other) must have a node at the closed end and an antinode at the open end. This geometric constraint only allows odd harmonics:

λn = 4L / n, fn = nv / 4L (n = 1, 3, 5, …)

The practical MCAT tip: closed pipe → odd harmonics only, and the fundamental wavelength is 4L instead of 2L — a closed pipe of the same length as an open pipe therefore has a lower fundamental frequency (by a factor of 2) and is missing every even harmonic.

Ultrasound

Ultrasound is sound with frequency above about 20,000 Hz — beyond the upper limit of human hearing. Diagnostic ultrasound imaging sends short pulses of high-frequency sound (typically 1–20 MHz) into the body and detects echoes reflected at boundaries between tissues of differing acoustic impedance Z = ρv (density × speed of sound). The fraction of intensity reflected at an interface grows with the mismatch in Z between the two tissues; large mismatches (soft tissue ↔ bone, soft tissue ↔ air) produce strong echoes and also strong shadowing beyond the interface, which is why ultrasound images bone poorly and why air-filled lungs scatter the beam. Gel is applied between the transducer and skin precisely to eliminate the air gap that would otherwise reflect almost all of the energy before it entered the body.

Echo timing and strength build a real-time image of depth and tissue interfaces. Because ultrasound uses non-ionizing mechanical waves rather than X-rays, it is considered safe for imaging during pregnancy. Combined with the Doppler Effect, it also directly measures blood-flow velocity and direction (Doppler ultrasound / echocardiography) — the classic double-shift case from a moving reflector (red blood cells).

Shock Waves

When a source moves through a medium faster than the wave speed itself (i.e., faster than the speed of sound — "supersonic"), the source outruns its own wavefronts. Instead of spreading in expanding circles, the wavefronts pile up and constructively interfere along the edges of a cone trailing the source, forming a shock wave. The audible result when this cone sweeps past a stationary observer is a sonic boom. Because vs > v breaks the Doppler formula above (the denominator would go negative), shock waves are treated as a distinct high-yield regime rather than an extreme case of ordinary Doppler shift.

Worked Example: Doppler Shift

An ambulance siren emits a steady tone at f = 500 Hz. It approaches a stationary pedestrian at vs = 34 m/s. Take the speed of sound as v = 340 m/s (a clean, MCAT-friendly round number close to the real ~343 m/s).

Because the source is approaching a stationary observer, use f' = f × v / (v − vs):

f' = 500 × 340 / (340 − 34) = 500 × 340 / 306 = 170,000 / 306 ≈ 556 Hz

No-calculator shortcut: notice vs/v = 34/340 = 1/10 here. For a source speed that is a small fraction of the wave speed, the exact fraction v/(v − vs) is well approximated by (1 + vs/v) — a first-order (binomial) approximation valid when vs ≪ v:

f' ≈ f × (1 + vs/v) = 500 × (1 + 0.1) = 500 × 1.10 = 550 Hz

The approximation (550 Hz) lands within about 1% of the exact value (556 Hz) — close enough for MCAT purposes, and it requires nothing harder than multiplying by 1.1 in your head. As the ambulance passes and moves away, the same logic with a plus sign in the denominator (f' = f × v/(v + vs) = 500 × 340/374 ≈ 455 Hz) reproduces the familiar falling pitch of a passing siren.

Common MCAT Traps

• Forgetting sound needs a medium. A passage set in space, or asking about sound "through a vacuum," is testing whether you remember sound cannot propagate without matter — light can, sound cannot.
• Reversing the Doppler sign convention. Always sanity-check by asking whether source and observer are approaching (frequency must go up) or receding (frequency must go down) before trusting the algebra.
• Assuming density alone determines sound speed. Students often expect denser media to be slower, but stiffness (elastic/bulk modulus) is the dominant factor — that's why sound is fastest in rigid solids, not slow, dense liquids.
• Mixing up open- and closed-pipe harmonics. Only a pipe closed at one end is restricted to odd harmonics with fundamental 4L; an open pipe (or a string) behaves like the 2L, all-integer-harmonic case.