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.
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.
Membranes with fixed edges also vibrate in modes. Their natural frequencies are not so simply related.
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.
Standing wave phenomena can also occur in a room at specific frequencies called the resonance frequencies of the room.