Standing wave

• What occurs when two waves overlap moving in opposite directions?

  Standing wave
• What is produced by the interference of two waves?

  Pattern of nodes and anti-nodes
• What are nodes in a standing wave?

  Regions of destructive interference
• What are anti-nodes in a standing wave?

  Regions of maximum displacement
• What must the frequency of the source correspond to for a standing wave on a string?

  Integer number of half wavelengths
• What are the different modes of oscillation in standing waves called?

  • First harmonic (fundamental mode)
  • Second harmonic
  • Third harmonic
  • Fourth harmonic
• What is an example of a standing wave?

  Guitar string being plucked
• What happens to a wave on a guitar string when it is plucked?

  It reflects and travels back and forth
• What is the equation for wave speed on a string?

  v = sqrt(T/μ)
• What is linear mass density?

  Mass per unit length of the string
• How does the length of a pipe affect sound frequency?

  Longer pipe produces lower frequency
• What type of waves are produced in pipes?

  Longitudinal waves
• What is the rule for standing waves in pipes?

  Open end is anti-node, closed end is node
• What is natural frequency?

  Frequency at which a system naturally vibrates
• What is a free oscillation?

  Oscillation at natural frequency without driving force
• What is a forced oscillation?

  Oscillation with a consistent driving force
• What is an example of forced oscillation?

  Vibration of a vehicle when engine runs
• What is resonance?

  Large amplitude oscillation at natural frequency
• How does resonance work with a swing?

  Push at right time for higher swings
• How do microwaves create thermal energy in food?

  By matching natural frequency of water molecules
• What happens when energy is applied at a frequency different from natural frequency?

  Amplitude of oscillations is considerably lower
• What are undesirable effects of resonance in mechanical systems?

  Can lead to fatigue and failure
• How can resonance affect bridges?

  Can cause collapse at specific wind speeds
• How do modern bridges mitigate resonance effects?

  By using dampers to absorb energy
• How do buildings mitigate earthquake effects?

  By fitting dampers to absorb vibrations
• What are the applications of standing waves and resonance?

  • Musical instruments
  • Calculation of wave speed
  • Engineering designs to prevent failure
• What is the relationship between wave speed, tension, and linear mass density?

  • Wave speed (v) is calculated as:

  $v =$$\sqrt{\frac{T}{\mu}}$

  • Tension (T) affects wave speed
  • Linear mass density (μ) influences wave speed