Question

How are standing waves and resonance applied to musical instruments?

Answer 1

Hint: Loud sound is produced in musical instruments or in liquid column or in air column when frequency of sound waves become maximum and this maximum frequency condition is achieved at resonance. All musical instruments produce stationary waves in different modes of vibrations.

Complete answer:
Musical Instruments are designed to produce stationary and standing waves. Organ pipe is the simple musical instrument in which sound is produced by setting an air column into vibrations. When air is blown into the pipe through the small hole, it strikes against the slanting surface. The sound waves travel gets reflected at its closed/open end, producing longitudinal stationary waves. If the frequency of these waves is equal to the frequency of edge tone, resonance occurs and aloud sound is produced. So standing waves are themselves an example of resonance.
So it is concluded that Standing waves only occur at specific frequencies which are related to the natural frequency of the oscillating system, e.g. guitar string, clarinet air column. So the resonance phenomenon is allowed for musical notes to be produced on a musical instrument.
A guitar is a special musical instrument which makes an additional use of resonance. The body of the guitar is carefully designed to resonate when notes are played on the strings. The reason is that the body can then behave as an amplifier for the strings.

Additional Information:
When two identical waves of same amplitude and frequency travelling in opposite directions with same speed along the same path superpose each other, the resultant wave does not travel in either direction and it is called stationary wave or standing wave.

Note:
The standing waves in a wind musical instrument are different from a vibrating string instrument. The wave on a string is a transverse wave, moving the string back and forth, rather than moving up and down along the string. But the wave inside a tube of air column is a longitudinal wave; the waves do not go from side to side in the tube. Instead, they form along the length of the tube.