Waves, Sound and Light

Waves tie together sound, light, radio and the rest of the electromagnetic spectrum, and the whole topic runs on a single relationship between three quantities.

Wave anatomy

Enlarge

Zoom in

Amplitude is measured from the rest position, not crest to trough. Crest to trough is twice the amplitude, and a question giving you that distance wants you to halve it.

Amplitude is what carries energy. For sound that means volume; for light it means brightness.

The wave equation

Speed = frequency x wavelength.

The consequence worth carrying: at a fixed speed, frequency and wavelength are inversely related. Double the frequency and the wavelength halves.

That single relationship answers a large share of the questions in this topic and in radio on Electronics Information.

Transverse and longitudinal

Transverse waves move the medium perpendicular to the wave's direction. Light, and a wave on a rope.

Longitudinal waves move the medium along the wave's direction, in compressions and rarefactions. Sound is longitudinal, and it is the example the test uses.

Sound

Sound requires a medium. It is the vibration of particles, so with no particles there is no sound. There is no sound in space, which is the most asked fact in this topic.

Speed of sound in air is about 343 meters per second, roughly 761 miles per hour at ordinary conditions.

Sound travels fastest in solids, slower in liquids, slowest in gases, because closely packed particles pass the vibration on more quickly. That ordering is the opposite of most people's intuition and is therefore asked.

Sound travels faster in warmer air, because the particles are moving faster to begin with.

Human hearing runs roughly 20 Hz to 20,000 Hz. Above that is ultrasound; below is infrasound.

The Doppler effect is the change in perceived frequency when a source moves relative to you. An approaching siren sounds higher because the waves arrive bunched together; a receding one sounds lower. The source's actual frequency does not change - only what reaches your ear - and that distinction is the question.

An echo is reflected sound. Because light is so much faster, you see distant lightning before you hear thunder, which is the standard application.

Sound spreads out as it travels, so it weakens with distance - and faster than you might guess. Double your distance from a source and the sound's intensity drops to one fourth, not one half, because the same energy is spread over four times the area. That square is the whole trick of the question.

Light

Light needs no medium and travels fastest in a vacuum, at about 300,000 kilometers per second, or 186,000 miles per second.

Light slows down in a denser material, which is the opposite of sound's behavior. Sound likes a dense medium; light is hindered by one.

The electromagnetic spectrum

Enlarge

Zoom in

The order, from longest wavelength to shortest:

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.

Wavelength decreases and frequency and energy increase as you go along that list. So gamma rays are the highest energy and radio the lowest, which is why gamma rays are dangerous and radio waves are not.

All of them are the same phenomenon and all travel at the speed of light. They differ only in wavelength.

Visible light is a narrow band in the middle. Within it, red has the longest wavelength and violet the shortest - which is why infrared sits just beyond red and ultraviolet just beyond violet. The names say where they are.

Infrared is felt as heat. Ultraviolet causes sunburn. X-rays pass through soft tissue. Those three uses are the ones the test names.

Reflection and refraction

Enlarge

Zoom in

Reflection: the angle of incidence equals the angle of reflection, both measured from the normal, the line perpendicular to the surface.

Refraction is the bending of light as it enters a new material, caused by the change in speed.

Entering a denser material, light slows and bends toward the normal. Leaving into a less dense material, it speeds up and bends away.

That is why a straw in a glass of water looks broken at the surface, and why a pool looks shallower than it is.

A prism separates white light into colors because each wavelength refracts by a slightly different amount. That separation is called dispersion, and it is also what a rainbow is - refraction and reflection in raindrops.

Total internal reflection happens when light inside a denser material hits the boundary at a steep enough angle that none escapes - it all reflects back in. It is what keeps light trapped inside fiber optic cables as they carry signals around corners.

Waves that meet, and waves that spread

Interference is what happens when two waves overlap: their displacements add. Crests meeting crests build a bigger wave - constructive interference. Crests meeting troughs cancel - destructive interference, which is exactly how noise-canceling headphones work. The swirling colors on a soap bubble are interference between light reflecting off the film's two surfaces.

Diffraction is waves spreading out as they pass through a narrow opening or around an edge. It is why you can hear someone talking around a corner you cannot see around: sound's long wavelengths bend around obstacles far more than light's short ones.

Scattering is why the sky is blue. Air molecules scatter short blue wavelengths much more than long red ones, so blue light reaches your eye from every part of the sky. At sunset the light crosses so much air that the blue is scattered away before it arrives, leaving the reds and oranges.

Polarized sunglasses cut glare by blocking light vibrating in one direction - the direction most light reflected off water and roads is vibrating in.

An object's color is the light it reflects, and it absorbs the rest. A red shirt reflects red. A white object reflects all visible wavelengths and a black one absorbs nearly all, which is why black absorbs more heat.

Mixing colored light

The primary colors of light are red, green and blue - the colors a screen is made of - and mixing light adds:

Paint works the other way. Pigments absorb colors rather than add them, so mixing paints darkens toward black, and the painter's primaries are different. A question about light wants the table above.

What you can skip

Across all 2,104 General Science questions in our bank:

• Lens and mirror equations. No question asks you to calculate a focal length or an image distance. Know converging from diverging and real from virtual.
• The critical angle and thin-film math come up once each, at the hardest difficulty.
• Decibel arithmetic appears once. Knowing that decibels measure loudness is enough.

Where people lose points

Saying sound travels through space. It cannot.

Saying sound travels fastest in air. Solids are fastest.

Saying light travels fastest in glass or water. A vacuum is fastest.

Reversing the spectrum order or thinking the bands travel at different speeds.

Measuring amplitude crest to trough.

Saying a red object absorbs red light. It reflects it.

Saying the Doppler effect changes the source's frequency.

Work one in under a minute

A wave has a frequency of 500 Hz and a wavelength of 0.7 meters. How fast is it traveling, and what is it likely to be?

Speed is frequency times wavelength: 500 times 0.7 is 350 meters per second.

That is very close to the speed of sound in air, so it is a sound wave.

Recognizing the number is the second half of the question, and 343 is worth knowing for exactly this reason.

Where this leads

The electromagnetic spectrum is what radio and antennas are built on, and the frequency-wavelength relationship carries directly into Electronics Information.