Two crests add constructively to make a larger amplitude.

A crest and trough add destructively to cancel out.

The first pair of frequencies has a harmonious 1:2 ratio.

I don't hate the second combination, but it does have a slight sour, tense, or sad sound to me. Of course, good music might find a place for that feeling.

This is the famous quantum mechanical double slit experiment.
Notice the alternating constructive and destructive interference pattern.

The cop will observe your light at a higher frequency and a shorter wavelength.

Star color is complex and could be caused by several different things.

An astronomer might use spectroscopy to figure out what's going on.

In a bottle, the air you blow sends a range of sound frequencies into the bottle, and many of those form standing waves. Adding more water smoothly transitions to higher frequencies because multiple standing waves are always available. This is why you don't have large gaps of silence, like in the simulation above.

There are 8 nodes if you count the edges.

There are 7 anti-nodes.

Waves can be in superposition. While the pulses overlap, the rope's observed displacement is the sum of the displacements from both pulses.

After the overlap, the pulses continue through each other. They do not bounce away like carts because the waves are not separate objects made of matter; they are disturbances moving through the medium.

This is constructive interference.

The two waves have displacements in the same direction at that location, so their amplitudes add. In water, that can make a higher crest or a deeper trough than either individual wave would make alone.

The headphone wave needs to be out of phase with the outside sound at your ear.

When a compression from the outside sound lines up with an opposite displacement from the headphone speaker, the waves add destructively. The superposition has a smaller amplitude, so the sound is quieter.

The air near your ear is in superposition from many sound waves at once. The observed pressure pattern is the sum of the different notes.

Your ear and brain can respond to the different frequencies inside that combined waveform. That is why a chord can be one physical wave pattern in the air but still be heard as multiple notes.

They are hearing beats. Beats happen when two similar frequencies interfere and the superposition alternates between more constructive and more destructive interference.

As the notes get closer to the same frequency, the beats slow down. When the notes match, the slow pulsing disappears.

This is diffraction. Waves spread after passing an edge or opening, so some sound bends into the region around the corner.

Sound has wavelengths that are large enough for everyday openings and corners to cause noticeable spreading. Visible light has much smaller wavelengths, so it usually does not spread around hallway corners in a way you can easily notice.

Each opening sends out waves that spread by diffraction. Those waves overlap on the screen.

Bright bands happen where the waves arrive in phase and interfere constructively. Dark bands happen where the waves arrive out of phase and interfere destructively.

This is the Doppler effect.

When the ambulance moves toward you, wave crests reach you more often, so the frequency you hear is higher and the wavelength is shorter. When it moves away, crests reach you less often, so the frequency is lower and the wavelength is longer.

Redshift suggests the galaxy is moving away from us.

For light, a longer observed wavelength is described as redshift. The page connects this idea to Hubble's observation that most galaxies are redshifted, which is evidence for an expanding universe.

The swing has a natural frequency. If the pushes match that timing, each push adds energy in a way that increases the amplitude of the motion.

That matching of the driving frequency to the natural frequency is resonance. The size of the oscillation grows because the pushes keep reinforcing the motion instead of fighting it.

The points that barely move are nodes. The points that move the most are antinodes.

They appear because waves reflect from the fixed ends and interfere with themselves. At the resonant frequencies, the superposition forms a standing wave instead of a wave pattern that simply travels down the string.

A positive CDR means the duckling experiences less wave drag than it would while swimming alone. At 100% or more, the wave drag has been reduced enough that the resulting wave force propels the duckling forward.

The spacing determines where each duckling sits within the combined waves. At the useful distance, the front of the duckling stays in a trough that produces a forward push. Matching the mother's speed keeps that position from drifting. With the wrong spacing or speed, the duckling moves out of the helpful part of the interference pattern and loses the boost.

During wave riding, interference between the mother's wave and a duckling's wave creates a force that propels the first ducklings forward. During wave passing, each duckling gathers wave energy and concentrates it behind itself, making that energy available to the next duckling. Wave passing helps the benefit continue even after the mother's own wave becomes smaller farther down the line.

The model predicts reduced wave drag for every duckling behind the mother, so it gives a physical reason that a line of boats might require less energy. However, it does not prove that full-size ships will receive the same benefit. Tests with realistic hull shapes, ship spacing, speeds, waves, and fuel use would be needed before reaching that conclusion.