Sound Waves & Beats
Sound is a crowd of air being squeezed rather than a wiggle going up and down, and beats are what two steady tones do when they nearly agree.
Introduction
Clap your hands and someone four metres away hears it a hundredth of a second later: something made that trip, but what?
You clap, and someone across the room hears it. What made the trip from your hands to their ear?
What travels
Displacement and pressure
Below the parcels the simulation draws two curves for the same air: how far each parcel is from home, and the pressure.
At the instant a particular parcel of air is exactly at its rest position, what is the pressure at that spot doing?
The pressure follows the slope of the displacement curve, turned over. Where neighbouring parcels crowd together, the pressure is above atmospheric; where they spread apart, it is below. So a displacement node is a pressure antinode.
The air sets the speed
Sound in air travels at
with in degrees Celsius: 331.3 m/s at freezing, about 343 m/s in a warm room. The medium owns the speed. The source only chooses the frequency, and then the wavelength is settled by
Louder is not higher
You slide the displacement amplitude s₀ from 3 µm to 12 µm and leave everything else alone. Which readouts change?
Two tones at once
Now two tones sound together. At every point and every instant their pressures add, and that is all interference ever is.
Two flutes hold 160 Hz and 170 Hz. You hear the loudness swell and fade ten times a second. What are the flutes doing during a swell?
Tuning by ear
Piano tuners use beats. Sound a tuning fork and the string together, listen for the beat, and adjust the string until the beats slow down and stop. That is a far finer measurement than judging either pitch on its own.
What comes next
You watched air pass a sound along without going anywhere, tuned a wavelength, and stopped a beat. So far every source has stood still. Next the source moves, and the pitch a listener hears stops being the pitch the source emits.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “A puff of air travels from the source to your ear”
- “Sound is a transverse wiggle, like a wave on a rope”
- “Louder means higher-pitched”
- “During beats one of the sources is sliding its frequency”
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Research behind this lesson
- Hrepić et al. 2010: Alongside the scientific wave model, introductory students hold an 'Entity' model in which sound is a self-standing thing distinct from the medium it travels through, plus hybrid models blending the two, which survive instruction.
- Linder & Erickson 1989: Phenomenographic clinical interviews with ten physics graduates entering a teacher-education programme, using everyday and school demonstrations of sound. Their conceptualizations included sound as a travelling entity rather than a disturbance of a medium: the earliest documentation of a conception that has since turned up in every study of how people think about sound.
- Wittmann et al. 1999: Students reason about a wave pulse as if it were an object, giving it the properties of a thrown ball, expecting the medium to travel with the disturbance.