4.3. Stationary Waves

• A stationary wave is formed when two progressive waves with the same frequency and amplitude travel in opposite directions
• At antinodes, crests and crests reinforce each other, resulting in maximum displacement
• Steps in the formation of stationary waves

  1️⃣ Two identical progressive waves travel in opposite directions.

  2️⃣ The waves superpose.

  3️⃣ At nodes, there is zero displacement.

  4️⃣ At antinodes, there is maximum displacement.
• At nodes in a stationary wave, the displacement is zero
• Stationary waves differ from progressive waves because they do not transfer energy
• What conditions are necessary for the formation of stationary waves?

  Same frequency and amplitude
• Stationary waves have uniform crests and troughs that move like progressive waves.

  False
• What is a defining characteristic of stationary waves compared to progressive waves?

  Fixed nodes and antinodes
• What happens to the crests and troughs of interfering waves at nodes in a stationary wave?

  They cancel each other out
• The pattern of nodes and antinodes in a stationary wave remains fixed in space.

  True
• Steps in the formation of stationary waves

  1️⃣ Two identical progressive waves travel in opposite directions

  2️⃣ Superposition of these waves

  3️⃣ Formation of nodes with zero displacement

  4️⃣ Formation of antinodes with maximum displacement
• In a stationary wave, nodes are located between antinodes
• Nodes in a stationary wave have zero displacement because crests and troughs cancel each other out.


  True
• A string fixed at both ends vibrates at its fundamental frequency and harmonic modes.


  True
• Microwave ovens use stationary waves of microwaves to heat food evenly.


  True
• Steps in the formation of stationary waves

  1️⃣ Two identical progressive waves travel in opposite directions.

  2️⃣ The waves superpose.

  3️⃣ At nodes, there is zero displacement.

  4️⃣ At antinodes, there is maximum displacement.
• The amplitude of a stationary wave varies between nodes and antinodes
• At nodes, crests and troughs cancel each other out, resulting in zero displacement
• How are stationary waves defined?

  Superposition of identical waves
• Steps in the formation of stationary waves

  1️⃣ Two identical waves travel oppositely

  2️⃣ Waves superpose

  3️⃣ Nodes form with zero displacement

  4️⃣ Antinodes form with maximum displacement
• What are the key differences between stationary and progressive waves in terms of energy transfer?

  No energy transfer in stationary waves
• In the formation of stationary waves, two identical waves travel in opposite directions along the same medium.
• At antinodes in a stationary wave, the crests of the waves reinforce each other.
• In a stationary wave, the displacement at nodes is zero
• Stationary waves do not transfer energy
• Match the characteristic with the correct feature of nodes and antinodes:

  Displacement ↔️ Nodes: Zero ||| Antinodes: Maximum

  Wave Interference ↔️ Nodes: Waves cancel out ||| Antinodes: Waves reinforce

  Location ↔️ Nodes: Fixed between antinodes ||| Antinodes: Fixed between nodes
• At antinodes in a stationary wave, the displacement is maximum
• In musical instruments, what is the principle behind creating specific tones using stationary waves?

  Vibration of strings or air columns
• Stationary waves do not transfer energy
• Stationary waves oscillate in fixed locations due to wave interference.


  True
• Stationary waves transfer energy through space.

  False
• At antinodes in a stationary wave, the displacement is maximum because crests reinforce each other.


  True
• Stationary waves involve net energy transfer.

  False
• The interference pattern in a stationary wave creates a fixed wave
• Why do stationary waves not transfer energy?

  Waves oscillate in fixed locations
• Nodes in a stationary wave have maximum displacement.

  False
• What are stationary waves also called?

  Standing waves
• What is the energy transfer like in stationary waves compared to progressive waves?

  No net energy transfer
• What is the amplitude of a stationary wave at antinodes?

  Maximum
• What type of interference occurs at nodes in a stationary wave?

  Destructive interference