Stationary and Progressive Waves

• A progressive wave is a wave that moves or propagates from one place to another
• If two progressive waves of the same frequency travel in opposite directions, a stationary wave is produced
• Stationary wave are not literally stationary, but in contrast to progressive waves, energy is stored and not transmitted.

• Antinode is where maximum displacement occurs
• Node is where no displacement occurs

1st Harmonic = F0, L = λ/2, λ = 2L

(1st Harmonic is the Fundamental mode of vibration, F0 is fundamental frequency)

2nd Harmonic = 2F0, L = λ, λ = 2L/3

3rd Harmonic = 3F0, L = 3λ/2, λ = L/2

4th Harmonic = 4F0, L = 2λ, λ = L/2

5th Harmonic = 5F0, L = 5λ/2, λ = 2L/5

1) Find frequency at which the oscilloscope registers minimum and maximum traces as the microphone is moved in the tube. This indicates the presence of standing waves.

2) Move the microphone until the oscillation trace is zero. This indicates a node. Note the distance to the speaker (L1)

3) Move the microphone away from the speaker until a second node has been found. Note the new distance to the speaker (L2)

4) Calculate the distance between the adjacent nodes (L2 - L1)

5) Adjacent nodes are always half a wavelength apart so L2 - L1 = λ/2 or λ = 2(L2 - L1)

6) Use the equation v = fλ [v = 2f (L2 - L1)]

For a stationary wave to occur you need to have waves that are:

• Same Speed
• Same Wavelength
• Same Frequency
• Travelling in opposite directions