• Standing Wave: A wave pattern that appears to stay in one place. It's a combination of two waves moving in opposite directions.
• Nodes: Points of no movement.
• Antinodes: Points of maximum movement.
• Harmonic: Multiple of the fundamental frequency.

Pipes can be

• Open at both ends 📭📭
• Closed at both ends 🚫🚫
• Open at one end, closed at the other 📭🚫

• Pipes open at both ends and closed at both ends

  • All harmonics (first, second, and so on) are present.
  • Number of half-wavelengths in the pipe increases by one with each harmonic.

• Pipes closed at one end

  • Odd harmonics (first, third, fifth, ...) are present.
  • Even-numbered harmonics (second, fourth, ...) are suppressed.

Frequency of a Harmonic

• For a pipe closed at one end
  • 📏 Length:\(L = \frac {3}{4} λ ⟹ λ = \frac {4L}{3} \)
  • 🎶 Frequency: \(f_3 = 32 λ ⟹ λ = \frac {2L}{3}\)
• For a pipe open at both ends
  • 📏 Length: \(L = \frac {3}{4} λ ⟹ λ = \frac {2L}{3} \)
  • 🎶 Frequency:\(f_3 = \frac {3c}{2L}\)
• Note: c is the speed of sound, and λ is the wavelength.