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They are alike in that both are waves. In physical mathematics, they can be described with partial differential equations that have a particular form, called a "wave equation." There are many particular wave equations, but they all have repeating patterns in space and time, and don't lose much energy in each cycle.

The difference between light and sound is the medium in which their waves travel.

Sound is a mechanical vibration. Atoms move, and the associated chemical bonds or molecules transmit the physical movement to other atoms. The motion is fastest in very rigid crystals such as diamond or steel (e.g. welded train rails). It is somewhat slower in liquids, like water, and slowest in gases, like air. In sea-level room-temperature air, sound moves at about 344 meters per second. In vacuum, with no air, sound cannot be transmitted. In each medium, there is a maximum "cutoff frequency." Beyond that number of cycles per second, the medium doesn't spring back fast enough to transmit the wave. It's about 100,000 cycles per second in air, and 12 million cycles per second in water. Sound waves can be bent by reflecting from rigid surfaces, or by arrays of tubes that slow the edges of the waves. Lower frequency sound waves can move larger, more rigid structures, so they reflect less easily from them. Frequencies below 10 cycles per second can move thin concrete walls.

Light is alternating magnetic and electrical waves at right angles (90 degrees) to each other. It is made when electric charges move rapidly. When the electrical wave grows it makes the magnetic wave. When the magnetic wave moves it makes the electrical wave. Different wavelengths are different spectral colors. Light is a very short wave, from 300 nanometers (hard ultraviolet) to 2000 nanometers (far infrared).

The waves move at the speed of light, about 300 million meters per second in vacuum. It moves slower when the electric fields have to move the electrons of atoms. Lenses bend the waves by slowing the edge of a wave, bending the fields. The longer (red) waves bend less easily, causing colors around the images in simple lenses. Rainbows form when light is bent by water drops. Light can also be reflected by electrical conductors (like aluminum, Mercury or silver) that short-out the electric fields with moving electrons. This causes the magnetic fields to reform as mirror images going in a mirror direction. In very intense magnetic fields, conductors become transparent because the electrons can no longer move to short out the electric fields of light.

In light from a hot place, like the sun or a filament light bulb, the waves are scrambled. Polarized light has the electric and magnetic components of the waves moving in the same direction. Lasers send polarized waves in lock-step (they are "coherent"), so that the electricity and magnetic fields reinforce each other.

Radio waves are much longer coherent waves from a few millimeters up to thousands of meters long. x-ray and gamma rays are much shorter waves, usually more like thermal light. As the waves get shorter, more intense electric fields are needed to reflect them. x-rays cannot be reflected by ordinary metals. They are reflected by the nuclei of heavy atoms, at angles of a few degrees.

All these "electromagnetic" waves are formed by moving electric charges: radio moves electrons in antennas, light moves electrons in atoms, x-rays and gamma rays are from moving particles in atomic nuclei. A human can make very long, weak radio waves just by getting a static electric charge on a comb, and waving it with their arm. Radio waves were first proven to exist with spark-gaps. Light, and gamma rays were proven to be electromagnetic because they are changed by strong electric and magnetic fields.

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Q: How are light and sound alike how are they different?
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