Summary
The nature of standing waves
Standing waves may be created from two waves travelling in opposite directions. Unlike travelling waves, they do not cause a net transport of energy.
String modes
Standing waves can be generated when plucking a string with fixed ends. Each mode has a wavelength and a corresponding frequency related to the length of the string.
Membrane modes
Membranes with fixed edges also vibrate in modes. Their natural frequencies are not so simply related.
Open-ended pipe
The natural vibrations of the air column in a pipe (like a flute) are due to standing waves or resonances. Air-reed instruments like the flute can be seen as a resonator excited by an air stream which flips in and out of the pipe at the resonant frequency of the system.
Room modes
Standing wave phenomena can also occur in a room at specific frequencies called the resonance frequencies of the room.