I think about it in terms of trading in time-frequency space. The total amount of time-frequency uncertainty is conserved: it's just like the Heisenberg uncertainty principle from physics, and is in fact deeply connected to it.
A classic Fourier spectrogram makes one choice about time uncertainty vs. frequency uncertainty and uses it for all frequencies. You can think of it as dividing time-frequency space into little squares that work okay for most quantities of interest.
Wavelets alter that tradeoff. At low frequencies, we often care about small differences in frequency (e.g., 4 vs 5 Hz), while the precise location of the peaks (e.g., 10 vs 10.1 s) matters less because the signal is changing slowly anyway. The situation is reversed at high frequencies: 1 kHz vs 1.001 kHz is often physically irrelevant, but the timing matters because they're so short). We therefore divide the time-frequency space up so that the windows are long in time, but narrow in frequency at low frequencies, square in the middle, and short in time but wide in frequency at higher ones.
On top of that, wavelets recognize that sine waves are a mathematically convenient basis, but may not reflect your data, so you can also swap in a "mother wavelet" that better matches whatever phenomena you're studying.
A classic Fourier spectrogram makes one choice about time uncertainty vs. frequency uncertainty and uses it for all frequencies. You can think of it as dividing time-frequency space into little squares that work okay for most quantities of interest.
Wavelets alter that tradeoff. At low frequencies, we often care about small differences in frequency (e.g., 4 vs 5 Hz), while the precise location of the peaks (e.g., 10 vs 10.1 s) matters less because the signal is changing slowly anyway. The situation is reversed at high frequencies: 1 kHz vs 1.001 kHz is often physically irrelevant, but the timing matters because they're so short). We therefore divide the time-frequency space up so that the windows are long in time, but narrow in frequency at low frequencies, square in the middle, and short in time but wide in frequency at higher ones.
On top of that, wavelets recognize that sine waves are a mathematically convenient basis, but may not reflect your data, so you can also swap in a "mother wavelet" that better matches whatever phenomena you're studying.