Waves & Sound
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flagWhat you'll discover
- arrow_forwardIdentify amplitude, wavelength, frequency and speed on a moving wave
- arrow_forwardUse v = fλ to predict how wavelength changes with frequency
- arrow_forwardBuild standing waves and locate their nodes and antinodes
- arrow_forwardSuperpose two waves and explain constructive and destructive interference
The anatomy of a wave
A wave is a travelling disturbance that carries energy without carrying matter. Its amplitude is the maximum displacement from rest, the wavelength λ is the distance between successive crests, and the frequency f is how many complete oscillations pass a point each second, measured in hertz (Hz).
These are tied together by the wave equation v = fλ: speed equals frequency times wavelength. On a given string the speed is fixed by tension and mass, so raising the frequency must squeeze the wavelength shorter — exactly what you will see when you move the frequency slider.
Superposition and interference
When two waves meet, they simply add: the displacement at every point is the sum of the individual displacements. This is the principle of superposition, and it produces interference.
Where crest meets crest, the waves reinforce into a bigger wave — constructive interference. Where crest meets trough, they cancel — destructive interference, possibly leaving the string momentarily flat even while both waves are present. Switch the simulation to interference mode and watch the faint component waves combine into the bold resultant. Noise-cancelling headphones use destructive interference to silence engine rumble in real time.
Standing waves
Send a wave down a string fixed at both ends and it reflects back, overlapping with itself. At the right frequencies the two travelling waves lock into a standing wave: certain points called nodes never move at all, while the antinodes between them oscillate with maximum amplitude.
Only wavelengths that fit a whole number of half-wavelengths between the fixed ends survive — these are the harmonics. Every guitar string, sitar string and flute column plays notes selected by exactly this fitting condition, which is why instruments produce specific pitches rather than noise.
Frequency is pitch
Sound is a wave of pressure travelling through air at roughly 343 m/s. What your ear perceives as pitch is simply frequency: a low rumble might be 60 Hz, the musical note A above middle C is 440 Hz, and a shrill whistle can exceed 4000 Hz. Humans hear from about 20 Hz to 20,000 Hz.
Loudness, by contrast, corresponds to amplitude — a bigger pressure swing sounds louder at the same pitch. So the two sliders in this lab map directly onto music: frequency chooses the note, amplitude chooses the volume.