Wave Interference Simulation

About this experiment

When two dippers tap the water of a ripple tank in step, their circular ripples overlap. Where a crest meets a crest the water moves strongly; where a crest meets a trough the water stays almost still. The result is a fixed pattern of calm lines fanning out from between the sources. Change the separation and the wavelength, flip one source to vibrate opposite, and drag the probe to measure the path difference that decides what happens at each point.

Learning goals

State the principle of superposition for two overlapping waves
Explain constructive and destructive interference in terms of path difference
Predict how the number and spacing of nodal lines depend on wavelength and source separation
Explain why coherent sources are needed for a stable interference pattern
Relate the ripple tank pattern to two-slit interference of light and sound

How to use it

1Watch the ripples with the default settings. Find the calm lines where the water hardly moves.
2Drag the probe onto a calm line and read the path difference. Repeat on a line of strong motion. What do you notice about the numbers?
3Switch on Show nodal lines and compare them with the pattern. Then switch to Average strength.
4Increase the distance between the sources. How does the number of nodal lines change? Check it against 2d/λ.
5Increase the wavelength. Do the lines spread out or squeeze together?
6Set the sources to vibrate opposite. What happens along the centre line between them?

The model

Δ = r_{2} - r_{1} = mλ

Constructive interference (sources in step): the path difference is a whole number of wavelengths

Δ = (m + \frac{1}{2}) λ

Destructive interference: the path difference is a whole number plus half a wavelength

y = A_{1} cos (k r_{1} - ω t) + A_{2} cos (k r_{2} - ω t - ϕ)

Superposition: the surface height is the sum of both waves, with k = 2π/λ

d sin θ = (m + \frac{1}{2}) λ

Far from the sources, the nodal lines point in these directions (d is the source separation)

Assumptions

Both sources have the same frequency, the same strength and a fixed phase difference (coherent sources).
Each circular wave weakens as 1 over the square root of the distance, as ripples spreading over a surface do. The water has no friction and the tank has no walls, so there are no reflections.
The ripple speed is fixed at 20 cm/s for the animation. The pattern depends only on the wavelength and the separation.
Path difference is shown in wavelengths. Interference counts as constructive when it is within 0.08 of a whole number and destructive when it is within 0.08 of a half.

Try this in class

Q1Why is the centre line always a line of strong motion when the sources vibrate in step?
Q2Two speakers play the same note. Why do some places in a room sound quieter than others?
Q3How many nodal lines would you expect for sources 10 cm apart with a wavelength of 2 cm?
Q4Why do two separate torches not produce a visible interference pattern on a wall?
Q5Noise-cancelling headphones use destructive interference. What must the headphone produce?

Frequently asked questions

Does the energy disappear at a nodal line?

No. Energy is not destroyed; it is redistributed. Less energy arrives along the nodal lines and more along the lines of constructive interference, so the total is the same as without interference.

What is the difference between a nodal line here and a node on a string?

Both are places where two waves always cancel. On a string the two waves travel in opposite directions and make a standing wave. In a ripple tank the waves come from two sources, and the calm places form curves called hyperbolas.

How is this related to the double-slit experiment?

Each slit acts like one of the two sources. The bright and dark fringes on the screen are where the lines of constructive and destructive interference meet the screen, and the same condition d sin θ = mλ applies.