1. PHYS 103 / DHC 161 Physics of Musical Sound
Lecture 17
Standing waves and mode shapes

2. Standing waves in a string
Frequencies of standing waves follow the harmonic series!

3. Longitudinal wave mode shapes (pressure vs. displacement)
transverse wave
(guitar string)
longitudinal wave
(slinky... or sound)
displacement is side to side
displacement is up and down
tube of air
Are the ends
open or closed
on this tube??

4. Longitudinal wave mode shapes (pressure vs. displacement)
displacement node
displacement antinode
Figure obtained from

5. Effect of boundaries fixed-fixed fixed-free All harmonics are possible
Only odd harmonics are possible