Lecture 19: Standing Sound Waves and Musical Instruments

Visualization of Standing Sound Waves

Displacement and Pressure description of Standing Sound Waves

• In understanding standing waves, the most important aspect is boundary conditions
• For sound wave in a tube different physics work at open and closed end of the tube
• One may think that at open end the wave just propagates into the outside, but this is not so. Even at the open end the sound wave is reflected and standing wave is formed

Closed end	Open end
Can't be any displacement, so displacement wave has a node. But any pressure in the wave is freely matched by reaction force from the wall Closed end is displacement node and pressure antinode	Pressure must match outside pressure and can't fluctuate, so pressure wave has a node. Closed end is pressure node and displacement antinode
Displacement view	Pressure view
Displacement wave is fixed at closed end and free at open end	Pressure wave is fee at closed end and fixed at open end

Normal Modes of the Flutes and Clarinets

"Flutes" are musical instruments which are pipes with both ends open . Other examples are, e.g, some organs	"Clarinets" are musical instruments which are pipes with one open and one closed ends
"Flutes" normal modes are indentical to a string with fixed ends. λ = 2 L, 2L/2, 2L/3, ... 2L/n	"Clarinets" are different, as a string with one fixed and one free end Fundamental harmonic is twice longer for the same length. Even harmonics are absent. Allowed wavelegth are λ = 4 L, 4L/3, 4L/5, ... 4L/(2n+1)

What about saxophone ? Saxophone is a conical pipe !