Sound: Pressure in Flight (and a Build)
Pitch is frequency, loudness is amplitude, and a passing siren bends both rules audibly. Then: measure the speed of sound with a wall and a clap.
Builds on: 4.1 Waves: Motion Without Transport
The two dials of a sound
Pitch is frequency. A young ear spans roughly 20 Hz to 20,000 Hz (the top eroding with age and headphone habits); a piano runs 27.5 to 4,186 Hz. Doubling the frequency raises the note exactly one octave — music is arithmetic your ear does for free. Loudness is amplitude — how hard the air is squeezed. Ears handle such a vast range that loudness is measured on the logarithmic decibel scale: every +10 dB is ×10 in energy. A 100 dB club is not “a bit” above an 85 dB limit; it is over thirty times the power.
Sound needs stuff
Pressure waves need something to squeeze. In a vacuum: silence — the film explosions are a courtesy. And the stiffer and lighter the medium’s springs, the faster the wave: ~343 m/s in room air, ~1,480 m/s in water, ~5,000 m/s in steel. Cowboys in films press an ear to the rail because the steel delivers the train’s rumble long before the air does.
The Doppler effect
A siren passes and its pitch visibly droops — eeee-yooow. The siren never changed; the geometry did. Moving toward you, the source partly chases its own waves, packing crests closer: shorter λ, higher pitch. Moving away, it stretches them. The effect belongs to every wave: radar guns Doppler microwaves off your car, bats do it to moths, and the redshift of galaxies — light stretched by recession — is the Doppler clue that the universe expands.
The build: clap at a wall
Sound’s speed is slow enough to measure in a courtyard. Stand 40+ metres from a big flat wall, clap, and the echo returns after the round trip: t = 2d/v — at 50 m, about 0.29 s. Too quick to time well once — so borrow the pendulum trick: clap in rhythm with your own echoes, so each clap lands exactly on the previous echo’s return. Your rhythm period is then exactly the round-trip time. Time 20 claps, divide, and:
Ships, bats and ultrasound scanners all run your courtyard experiment at higher frequency: send a pulse, time the echo, multiply by the known speed to get distance. You are calibrating the ruler they all use.
⚗️ Lab — The Siren Flyby
A sound source you can drive past a listener, with the wavefronts drawn honestly.
- Park the source: perfect circles, steady pitch. Now drive — watch the circles crowd ahead and stretch behind.
- Read the heard frequency before and after the pass; the drop is the eeee-yooow.
- Push the source toward the speed of sound and watch the crests pile into a wall.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.