progressive and stationary waves

what is phase?

The phase of an oscillating particle at a certain time is the fraction of a full cycle it has completed since the start of its motion

How is phase expressed?

As an angle in degrees

Or radians

Phase difference could be between…

• 2 different points on the same wave

• 2 different waves

Conversions from degrees to radians

90 degrees - pi/2 rad

180 degrees - pi rad

360 degrees - 2pi rad

When are 2 points in phase

When there is one wave cycle between them or there is one wavelength between them

When are 2 points in antiphase?

When there is half a wave cycle or half a wavelength between them

Describe the motion of a particle in a stationary wave

(Full cycle starting at equilibrium)

The particle moves from the position of equilibrium up towards maximum displacement then down through the equilibrium position to the maximum downward displacement then back up to equilibrium.

What are the conditions needed for a stationary wave to form?

Two waves with:

• the same frequency

• similar amplitudes

• moving in opposite directions

What happens when the waves superpose?

The amplitudes are added together

What is a node?

A node is when there is zero vibration/ amplitude

What is an antinode?

When the vibrations are at maximum amplitude

State the principle of superposition

When two or more waves of the same type meet in one place the total displacement is the vector sum of the individual displacements

Energy transfer in a standing wave compared to a progressive wave

No energy transfer in a stationary wave

Energy transfer in a progressive wave

First harmonic length

Wavelength / 2

2nd harmonica length

= Wavelength

3rd harmonic length

=3 wavelength/2

4th harmonic length

2 x wavelength