2026-06-07 19:25

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Sound Extended

The sound barrier and sonic boom

• When an object velocity approaches the speed of sound and exceeds it, this causes a sonic boom.
  • $\to$ Buildup of sound waves at the tip of the object wont be able to keep pace with the object

Wave Interference

• Principle of superposition: When 2 or waves interfere, we add their displacements.

Constructive Interference

• Two waves added together cause a net increase, resulting in an antinode

Destructive Interference

• Two waves cancel each other out, resulting in a node

Standing Waves on a string (Transverse Wave)

Velocity of standing wave:

• $v=\sqrt{\frac{T}{\mu }}$ , T = tension (N) and $\mu$ = $\frac{m}{l}=\frac{kg}{m}$
• Only for transverse waves on a string

Air Columns - Longitudinal Sound Waves

$L_n=\frac{(2n-1)\lambda }{4}$, n = resonance length number

Open Column

$L_n=\frac{n\lambda }{2}$ $\to$ $\mathrm{\Delta }L=\frac{1}{2}\lambda$

Air Column Diagram:

Beat Frequency

• When two waves of relatively close frequency overlap
  • $\to$ New beats are created
• Frequency of beats:
  • $|f_1-f_2|$ , the rate of change of beat frequency/s

References

5.1 Sound