Lecture Notes: Velocity of Source and Wave

Introduction

• Previous discussions assumed the velocity of the source (object emitting a wave) is less than the velocity of the wave.
• Focus on understanding what happens when the velocity of the source equals the velocity of the wave.

Application of Formulas

• Observed Period and Frequency:
  • When the source’s velocity equals the wave’s velocity, the observed period becomes 0.
  • This implies no time between successive wave crests, creating a single impulse.
  • Frequency becomes undefined (0 denominator in formula), approaching infinity as source velocity nears wave velocity.

Conceptual Understanding

Doppler Effect Recap

• When moving slower than wave speed:
  • Crests released at intervals; observer experiences compressed wavelengths.
  • Observer closer experiences crests more frequently.

Source Moving at Wave Speed

• Current and historical positions of the source:
  • Current position: emits new crest.
  • Previous positions: crests have traveled outward at source’s velocity.
• All wavefronts converge at the same point simultaneously.
• Observer’s Experience:
  • Rather than periodic sound, observer hears all wave energy simultaneously.
  • Perceived as a "thump," not a continuous sound pitch.

Application to Sound Waves

Sonic Boom

• When moving to supersonic speeds (past trans-sonic range), a sonic boom occurs.
• All sound energy reaches the observer at once, causing this phenomenon.

Conclusion

• Understanding phenomena like sonic booms require recognizing how wavefronts converge when source and wave velocities align.
• Future discussions will explore more on the sonic boom and mach numbers.

Note

• While the discussion used sound waves for visualization, the principles apply to any type of wave.