This unit is about waves, which are disturbances that transfer energy from place to place. In many waves, the medium oscillates with little net movement along the wave's path. By the end, you should be able to classify a wave, read its amplitude, wavelength, frequency, and period off a graph, use , and predict what happens when two waves overlap.
Read the overview first to get the big picture, then work through each topic note and try its checkpoint question before checking the answer.
Waves show up all over physics, from sound and light to earthquakes and guitar strings. This unit gives you vocabulary and equations for describing basic wave properties. Later topics like sound, light, and optics build directly on what you learn here.
Honors Physics Unit 13 covers what waves are and how to describe them. You start by sorting waves into mechanical (need a medium, like sound) and electromagnetic (can cross a vacuum, like light), and into transverse (the disturbance is perpendicular to the wave's direction) and longitudinal (the disturbance is parallel to the wave's direction). Next you learn the measurable properties of a wave, which are amplitude, wavelength, frequency, period, and speed, and how they connect through and . The unit ends with superposition and interference, including constructive and destructive interference and standing waves with nodes, antinodes, and harmonics.
When a wave passes through a rope or the air, each bit of the medium oscillates around its rest position and hands energy to its neighbor. A cork on a pond bobs as ripples pass rather than moving along with them at the wave's speed. Waves transfer energy, although some waves can also cause net movement of matter.
Sound moves at about 343 m/s in room-temperature air no matter what note is playing. If the speed is fixed, means a higher frequency must come with a shorter wavelength. For ordinary, small-amplitude sound waves in the same air, changing amplitude changes the energy carried but not the wave speed.
For waves in a linear medium, the displacement at any point is the sum of what each wave would produce alone. Crest on crest makes a bigger crest, and equal crest and trough displacements can cancel. In an ideal linear medium, the waves continue unchanged after they pass through each other.
A wave's type, amplitude, wavelength, frequency, and speed describe its basic properties. To find the result when linear waves overlap, add their displacements at each point; their relative phase matters. On a guitar string, two waves traveling in opposite directions form a standing-wave pattern with fixed nodes.
A wave is a disturbance that carries energy through space.
Five quantities describe a periodic wave.
The principle of superposition says that when waves overlap in a linear medium, the total displacement at each point is the sum of the individual displacements, y = y_1 + y_2.
A wave is a disturbance that carries energy through space. You can classify waves by whether they need a medium and by the direction of their disturbance. Some waves have both transverse and longitudinal motion.
The first question is whether the wave needs a medium. Mechanical waves travel through matter, like sound in air, ripples on water, or seismic waves in rock. Electromagnetic waves such as light, radio, and X-rays can cross empty space, which is why sunlight reaches Earth through the vacuum of space.
The second question is how the disturbance is oriented compared with the wave's direction. In a transverse wave, the disturbance is perpendicular to that direction, like a rope shaken up and down while the wave runs sideways. Light is also transverse: its electric and magnetic fields oscillate perpendicular to its direction of travel. In a longitudinal mechanical wave, particles move back and forth along the wave's direction, creating compressions and rarefactions. Sound in air is longitudinal.
One correction to a common claim: surface water waves aren't purely transverse. Water particles move in roughly circular paths, so they have both up-and-down and forward-and-back motion.
A pulse is a single disturbance, like one flick of a rope. A periodic wave is a repeating pattern, like the nearly steady tone of a tuning fork. A simple periodic wave has a single frequency and wavelength; a pulse can contain a range of frequencies and wavelengths.
Check yourself: Astronauts on the Moon can see each other's lights but can't hear each other shout without radios. Why? (Answer: Light is an electromagnetic wave and can cross the vacuum, but sound is a mechanical wave and needs air or another medium to travel.)
| Feature | Transverse wave | Longitudinal wave |
|---|---|---|
| Direction of disturbance | Perpendicular to wave direction | Parallel to wave direction |
| Visible features | Crests and troughs | Compressions and rarefactions |
| Examples | Light, wave on a rope, seismic S-waves | Sound in air, slinky pushed along its length, seismic P-waves |
| Travels through fluids? | Light can; ordinary fluids do not support transverse mechanical waves in their interior | Yes, through solids, liquids, and gases |
Five quantities describe a periodic wave. Amplitude is the maximum displacement from the rest position, measured from the midline to a crest for a sinusoidal wave, not from crest to trough. Wavelength is the length of one full cycle, such as crest to crest. Frequency is how many cycles pass a point each second, in hertz. Period is the time for one cycle, and . Wave speed connects them through .
The medium and its conditions affect wave speed. Sound travels about 343 m/s in room-temperature air, about 1,480 m/s in water, and about 5,960 m/s in steel. If wave speed is independent of frequency, changing the frequency changes the wavelength but not the speed. In a dispersive medium, speed can also depend on frequency.
Amplitude relates to energy. For a given wave type, frequency, and medium, the energy carried is proportional to amplitude squared, so doubling the amplitude gives four times the energy. For ordinary sound waves in the same air, a louder sound has a larger amplitude but the same speed.
Worked example. A tuning fork plays 440 Hz in air where sound moves at 343 m/s. Find the wavelength and period. Wavelength: m. Period: s, or about 2.3 ms. If you switch to an 880 Hz fork, the speed stays 343 m/s, so the wavelength halves to about 0.39 m.
Check yourself: A wave on a rope has a period of 0.25 s and a wavelength of 2.0 m. What is its speed? (Answer: f = 1/0.25 = 4.0 Hz, so v = fλ = 4.0 × 2.0 = 8.0 m/s.)
The principle of superposition says that when waves overlap in a linear medium, the total displacement at each point is the sum of the individual displacements, . Signs matter. If one wave is at +3 cm and another is at −1 cm at the same point, the medium sits at +2 cm. In an ideal linear medium, each wave continues unchanged after they pass.
In constructive interference, overlapping displacements reinforce each other. In destructive interference, they partly or completely cancel. For waves of the same frequency, perfect alignment makes their amplitudes add, while a half-cycle phase difference makes them subtract. Two equal waves perfectly out of phase cancel completely where they overlap. Noise-canceling headphones use destructive interference.
A standing wave forms when two waves of equal frequency and amplitude travel in opposite directions, usually a wave and its reflection. Nodes have zero displacement, antinodes oscillate with the largest amplitude, and adjacent nodes are apart. For an ideal string of length fixed at both ends, only certain frequencies fit: the harmonics have and . Other systems can have standing-wave frequencies that are not whole-number multiples of the lowest frequency.
Worked example. A 0.65 m guitar string has wave speed 400 m/s. The fundamental has m, so Hz. The third harmonic is Hz, with m.
Check yourself: A 5 cm upright pulse and a 2 cm upright pulse overlap peak to peak on a rope. What is their combined displacement? What if the 2 cm pulse is inverted instead? (Answer: When both are upright, the displacement is 5 + 2 = 7 cm. With the 2 cm pulse inverted, it is 5 − 2 = 3 cm.)
| System | Displacement at ends | Harmonics present | Wavelength of nth harmonic |
|---|---|---|---|
| String fixed at both ends | Node and node | All (n = 1, 2, 3, ...) | λ = 2L/n |
| Pipe open at both ends | Approximate antinode at each opening | All (n = 1, 2, 3, ...) | λ = 2L/n |
| Pipe closed at one end | Node at the closed end; approximate antinode at the opening | Odd only (n = 1, 3, 5, ...) | λ ≈ 4L/n, where L is the effective length |
| Term | Definition |
|---|---|
| Wave | A disturbance that transfers energy from one place to another, often with little net transport of matter. |
| Medium | The material, such as air, water, or a rope, that a mechanical wave travels through. |
| Transverse wave | A wave in which the disturbance is perpendicular to the direction the wave travels, such as displacement on a rope or the electric field in light. |
| Longitudinal wave | A wave in which the disturbance is parallel to the direction the wave travels. In sound moving through air, the disturbance produces compressions and rarefactions. |
| Wavelength | The distance covered by one full cycle of a wave, such as from one crest to the next. |
| Hertz | The unit of frequency, equal to one cycle per second. |
| In phase | Describes two waves whose crests and troughs line up, which leads to constructive interference. |
| Standing wave | A vibration pattern with fixed nodes and antinodes, formed by two identical waves traveling in opposite directions. |
| Harmonic | One of the specific frequencies at which a standing wave can form, each a whole-number multiple of the fundamental for strings and open pipes. |
Since has in it, it's tempting to think raising always raises . If speed is fixed, raising frequency shortens the wavelength instead. Wave speed depends on the medium and its conditions; in a dispersive medium, it can also depend on frequency.
On a graph, the crest-to-trough distance is the most obvious size, but that's twice the amplitude. Amplitude is measured from the midline (equilibrium) to a crest or to a trough.
Standing wave diagrams show loops, and one loop looks like one wave. One loop is only half a wavelength, so adjacent nodes are apart. A full wavelength takes two loops.
When displacements cancel at one point, energy is not destroyed. Energy can be redistributed through the medium or exchanged with the sources, depending on the setup. In an ideal linear medium, waves continue unchanged after they pass through each other.