One shape can hide many frequencies.
A wave can look complicated in one representation and simple in another. This lab lets you move between time, space, frequency, modes and samples—and see what information is preserved or lost when the representation changes.
Build a waveform from harmonics.
Fourier analysis represents suitable periodic signals as sums of sinusoids. Change the amplitudes below and watch the waveform and its frequency spectrum update together.
Boundaries choose the standing modes.
A string cannot vibrate arbitrarily when its ends impose constraints. The allowed spatial patterns are eigenmodes of the boundary-value problem.
Localize a pulse, broaden its spectrum.
A narrow Gaussian packet requires a wider range of spatial frequencies. This is a mathematical Fourier tradeoff, closely related in form to uncertainty relations that appear in wave and quantum mechanics.
Sample too slowly, and different frequencies become indistinguishable.
The Nyquist limit is an information boundary. Once a signal is sampled, frequencies above half the sampling rate can masquerade as lower frequencies.