Chapter 8: Wave in Pipes and Strings

8.1 Stationary Waves in Pipes

8.2 Harmonics and Overtones

• Open pipe: All harmonics (1st, 2nd, 3rd…) present
• Closed pipe: Only odd harmonics (1st, 3rd, 5th…) present
• Overtone: Frequency higher than fundamental frequency

8.3 End Correction

8.4 Velocity of Transverse Waves Along a Stretched String

8.5 Vibration of String and Overtones

8.6 Laws of Vibration of Fixed String

• Frequency ∝ 1/Length → longer string, lower pitch
  • Frequency ∝ √Tension → higher tension, higher pitch
  • Frequency ∝ 1/√μ → heavier string, lower pitch

Important Questions and Answers in Short

✅ Formula Sheet (Quick Revision)