(455) Standing waves [IB Physics SL/HL]

Standing Waves

• Standing waves are formed when two waves meet in superposition traveling in opposite directions.

• Key concepts:

  • Nodes: Points where there is no movement.

  • Anti-nodes: Points of maximum displacement.

Demonstration

• Using a string fixed at both ends, a pulse is sent and reflects off the ends.

• Adding more pulses demonstrates how waves interact through superposition.

Key Principles

• Maintain frequency and amplitude to create clear standing waves.

• The resulting pattern appears stationary due to the interference of the two waves.

Critical Equations

• Wave equation: V = F * λ (wave speed = frequency x wavelength)

Harmonics in Fixed Strings

• Fundamental Frequency (First Harmonic):

  • Length (L) = λ / 2

• Second Harmonic:

  • Length (L) = λ (1 wavelength)

• Third Harmonic:

  • Length (L) = (3λ / 2)

Harmonics in Closed-Open Systems

• Node at the closed end, anti-node at the open end.

• First Harmonic:

  • Length (L) = λ / 4

• Third Harmonic:

  • Length (L) = 3λ / 4

• Fifth Harmonic:

  • Length (L) = 5λ / 4

Harmonics in Open-Open Systems

• Anti-node at both ends.

• First Harmonic:

  • Length (L) = λ / 2

• Second Harmonic:

  • Length (L) = λ

• Third Harmonic:

  • Length (L) = (3λ / 2)

Example Problem

• For a pipe open at one end, if V = 330 m/s and F = 16 Hz:

  • Find wavelength (λ): λ = V / F -> 330 / 16 = 20.625 m.

  • Find length of the organ pipe (L = λ / 4): 20.625 / 4 = 5.15625 m, rounded to 5.2 m.