Sound — Print · Grade 12 Science

Sound

Learning goals

• I can describe sound as a longitudinal wave and relate pitch to frequency and loudness to amplitude.
• I can explain and calculate the Doppler effect and describe resonance and standing waves.

Readings for this unit

• A vibration record is not a picture of a wave traveling across a room

Sound is a longitudinal wave, and that single fact explains most of its behavior. Instead of the up-and-down motion of a rope, the particles carrying a sound wave vibrate back and forth along the same line the wave travels, squeezing into compressions where they crowd together and stretching into rarefactions where they thin out. A struck tuning fork, a vibrating speaker cone, or your own vocal cords launches this pattern of pressure ripples outward. Because sound is nothing more than particles jostling their neighbors, it absolutely requires a medium — which is why space is silent, and why the booming explosions in science-fiction films could never actually reach your ears across a vacuum.

Sound speed depends on the medium’s elastic properties, density, and conditions such as temperature. For small disturbances in a suitable approximately nondispersive model, it is not set by source loudness or pitch. Room-temperature air is often approximated near 343 m/s; use the value stated for a particular task. Many solids transmit sound faster than air, but closely spaced particles alone are not a sufficient explanation, and material properties must be considered.

Pitch is perception strongly related to frequency for simple tones. Intensity is sound power per area, while perceived loudness also depends on frequency, duration and listener. A sound-intensity level uses decibels: β=10log₁₀(I/I₀), with a stated reference. A 10 dB difference means tenfold intensity, not tenfold perceived loudness. A pressure-amplitude ratio uses a different logarithmic factor under matched impedance conditions. Keep the physical and perceptual quantities distinct.

The Doppler effect compares emitted and received frequency. For a stationary receiver in still air and a subsonic source moving directly toward it, fobs=fsource v/(v−vs); recession uses v+vs. Source and receiver velocities are relative to the medium and the formula depends on geometry. Vacuum-light shifts use relativistic relations rather than simply substituting c into a sound formula; cosmic expansion adds another interpretive framework.

Standing-wave patterns can arise through suitable overlapping incident and reflected waves. Nodes have zero displacement amplitude and antinodes larger amplitude in the ideal pattern. Boundaries determine allowed modes. Driving near a natural frequency can produce resonance, while damping and coupling limit real amplitudes. A string and an air column have different displacement and pressure boundary conditions, so their harmonic patterns should not be transferred without checking those conditions.

Musical instruments combine source vibration, boundary-supported modes and energy loss. Walls transmit, reflect and absorb sound according to material, thickness, openings and frequency; a single “poor medium” label is insufficient. Sonar and biological echolocation use sound travel, while radar uses electromagnetic waves. Medical ultrasound uses acoustic interactions with tissues under controlled professional equipment and protocols; this course uses diagrams and supplied records rather than requiring exposure experiments.

Model check: Sound requires a medium; pitch and loudness measure different aspects. Round-trip 170 m; one-way distance 85 m.

Distance from Speed and Time

d = v × t

v is the speed of sound (about 343 m/s in air); t is time in seconds; d is distance in meters. For an echo, the sound covers 2d, so d = v × t ÷ 2.

Doppler Effect (moving source)

f′ = f × v ÷ (v ∓ vₛ)

f′ is the observed frequency; f is the source frequency; v is the speed of sound; vₛ is the source's speed. Use the minus sign when the source approaches, the plus sign when it recedes.

Fundamental Frequency (resonance)

f₁ = v ÷ (2L)

f₁ is the lowest resonant (fundamental) frequency of a string fixed at both ends or an open pipe of length L; v is the wave speed. Higher harmonics are whole-number multiples of f₁.

Worked examples

Avoid these mistakes

• Sound requires a medium; pitch and loudness measure different aspects.

Words to know

longitudinal wave

A wave in which particles vibrate back and forth in the same direction the wave travels, creating compressions and rarefactions.

pitch

How high or low a sound is perceived; determined by the sound wave's frequency.

loudness

How intense a sound seems; determined by the wave's amplitude and measured on the logarithmic decibel (dB) scale.

medium

The matter — solid, liquid, or gas — that a mechanical wave such as sound must travel through.

Doppler effect

The change in observed frequency (pitch) when a wave source and observer move relative to each other.

resonance

The large-amplitude vibration that occurs when a system is driven at its natural frequency.

standing wave

A stationary wave pattern of fixed nodes and antinodes formed when a wave reflects and interferes with itself, as on a guitar string.

Sound is faster in steel than air — and instant in neither

A common misconception is that sound is effectively instantaneous; in fact it travels at a definite, medium-dependent speed. In room-temperature air that is about 343 m/s, but in water roughly 1,480 m/s and in solid steel around 5,900 m/s — because tightly packed particles hand off the vibration far faster. That is why railroad workers in old films pressed an ear to the rail: the steel delivers the sound of an approaching train sooner and farther than the air. Temperature matters too — warmer air carries sound a little faster, since its molecules move more quickly.

Christian Doppler, Buys Ballot, and a trainful of trumpeters

In 1842 the Austrian physicist Christian Doppler predicted that a moving source should shift the pitch a listener hears. Three years later the Dutch scientist Buys Ballot staged one of science's most charming tests: he had trumpeters play a sustained note aboard an open railway car speeding past musicians with perfect pitch, who confirmed the note rose as the car approached and fell as it receded — exactly as Doppler foretold. The same effect, applied to light, later let astronomers discover that distant galaxies are rushing away, evidence for an expanding universe.

Decibels are logarithmic: why 'twice as loud' isn't twice the number

Loudness is measured on the decibel (dB) scale, and — like pH — it is logarithmic, not linear. Every 10 dB marks a tenfold jump in sound intensity, so a 60 dB conversation and a 110 dB rock concert differ by 50 dB, which is 10⁵ — about 100,000 times more intense, not 'roughly twice.' This is why loud sound damages hearing so much faster than people expect, and why safety limits on headphones and workplaces are written in decibels: a few extra dB hides a huge jump in the actual energy hitting your eardrum.

Resonance can shatter a glass — and rattle a bridge

Every object has natural frequencies at which it 'wants' to vibrate. Drive it at one and the amplitude builds enormously — resonance. A trained singer sustaining a note at a wine glass's natural frequency can feed it energy until it shatters; a child pumping a swing in rhythm climbs higher and higher on the same principle. Engineers respect resonance too: the 1940 collapse of the Tacoma Narrows Bridge, whose deck twisted itself apart in a moderate wind, is the textbook cautionary tale (its cause is better described as aeroelastic flutter, but it made resonance famous).

Echolocation and ultrasound: seeing with sound

Sound above 20,000 Hz — ultrasound — is inaudible to humans but immensely useful. Bats and dolphins echolocate, emitting rapid ultrasonic pulses and reading the returning echoes to map size, distance, and even the texture of prey in total darkness. We borrowed the trick: sonar lets ships and submarines 'see' the seafloor, and medical ultrasound images a developing fetus or a beating heart safely, using no radiation at all — just the timing and strength of reflected pressure waves, the very same physics that makes an echo bounce off a canyon wall.

In the real world

Doppler weather radar bounces microwaves off raindrops and reads the frequency shift of the return to measure how fast a storm's winds are moving toward or away from the station.

Exit check

An echo returns after.50 s at 340 m/s. Find wall distance.