Interference.

Step 1 of 5

Two waves meet

Now the tank has two beads on the same arm. They tap together, at the same frequency, and send out identical rings. The wave speed in this tank is 25 cm/s, and time is slowed down, as before.

Where two waves meet, their displacements add: the height of the water is the sum of the heights each wave would give on its own. This is the principle of superposition. Crest and crest give a double crest: constructive interference. And crest and trough?

Step 2 of 5

The path difference

Choose On under Show the calm lines: the calm water is tinted orange. To tell whether a point is calm, measure its distance from each of the two beads. The difference between the two distances is the path difference, $\Delta$⁠.

• When $\Delta$⁠ is a whole number of wavelengths, $0, \lambda, 2\lambda, \dots$⁠, the two waves arrive in step: crest with crest. The water there swings strongly.
• When $\Delta$⁠ is half a wavelength, one and a half and so on, $\tfrac12\lambda, \tfrac32\lambda, \dots$⁠, a crest always arrives with a trough: destructive interference, and the water hardly moves.

At 10 Hz the wavelength is $\lambda = \dfrac{25}{10} = 2.5$$\lambda =$$\dfrac{25}{10} =$$2.5$⁠ centimetres.

Step 3 of 5

How many calm lines

Each value of $\Delta$⁠ that gives destructive interference traces a whole curve across the water, a nodal line: a calm line that starts between the beads. But the path difference can never be larger than the distance between the beads themselves: at the extreme, a point on the line through both of them, one is further than the other by exactly the Source separation. So only values of $\Delta$⁠ smaller than that distance make lines.

The source separation is 8 cm. You can count the orange lines in the Scene, and you can work it out.

Step 4 of 5

Further apart

Now the beads are closer together, 4 cm, and Source separation is free. Predict what will happen to the calm lines when the beads move apart to 12 cm.

Step 5 of 5

Only two lines

Exactly the same pattern appears in sound: two loudspeakers playing the same note make loud spots and quiet spots across a room, and noise-cancelling headphones play a sound that reaches the ear exactly half a cycle after the noise. And in light, Thomas Young saw bright and dark bands when he shone it through two slits.

The Frequency is fixed. Move the beads until only two calm lines are left.