Waves, light and sound

15

HintFive whole waves sweep past you every second, and each one is three metres long.

The whyWave speed = frequency × wavelength, so 5 × 3 = 15 m/s. Picture five waves passing every second, each three metres long: 15 metres of wave goes by each second. The same relationship holds for sound and for light, which is why a low note and a high note from the same instrument still reach you together.

Longitudinal

HintThe opposite of transverse: picture a slinky pushed and pulled from one end.

The whySound travels as particles squash together and spread apart along the line the wave moves, making compressions and rarefactions. A ripple on a pond is transverse instead: the water bobs up and down while the wave itself moves sideways across the surface.

It gets higher

HintTighten a guitar string and listen to what the note does.

The whyFrequency counts vibrations per second in hertz, and our ears report that as pitch. A young person hears roughly 20 Hz up to 20 000 Hz, and the top of that range falls away with age.

The amplitude

HintThe size of each vibration — how far the air is shifted every time.

The whyA bigger vibration moves more air, so more energy arrives at your ear. Loudness itself is reported in decibels, and anything above about 85 dB damages hearing if you stay in it.

300 metres

HintThe pulse makes the journey twice, so do not forget to halve what you work out.

The whyDistance = speed × time gives 1500 × 0.4 = 600 m, but that is the there-and-back trip, so the sea bed is 300 m down. Sound is the right tool because water carries it for kilometres, while light is absorbed within a few tens of metres. An echo off a cliff is timed in exactly the same way.

The eardrum

HintA tight skin stretched across the inner end of the canal.

The whyAir vibrations shake it, three tiny bones magnify the movement, and the cochlea turns that into nerve signals. Loud noise destroys the delicate hair cells inside, and that damage never heals.

Rays travel straight through the hole, so light from the top lands at the bottom

HintFollow one ray leaving the object's head, then another leaving its feet, and see where each finishes.

The whyBecause light cannot bend round the edge of the pinhole, a ray leaving the top of the object can only reach the lower part of the screen, and one leaving the bottom can only reach the upper part. The image is therefore inverted, and swapped left to right as well. Your eye forms its picture the same way, and your brain turns it the right way up.

reflection

HintA ray leaving a mirror tilts by as much as the one arriving did.

The whyBoth angles are measured from the normal — the line drawn at right angles to the mirror — not from the mirror surface itself. A snooker ball off a cushion obeys the same rule.

Changes speed, bends, straight — refraction at the surface fools the brain

HintFollow one ray from air into water and ask what the water does to it.

The whyLight slows on entering water or glass and speeds up again on leaving, and that is what bends its path. Your brain still assumes the rays came straight to you, so it draws the straw in the wrong place.

A spectrum of colours

HintThe same band you see arching over a rainy sky.

The whyWhite light is a mixture, and glass bends each part of it by a slightly different amount, fanning them out from red through to violet. Raindrops do exactly the same job in the sky.

It is absorbed

HintThe jumper only sends back its own colour; the rest goes no further.

The whyA coloured surface reflects its own colour and soaks up the others, so a red jumper under pure green light looks black. A filter works the same way, letting one colour through and blocking the rest.

About 340 metres per second

HintCount the gap between a lightning flash and the thunder that follows it.

The whySound is around a million times slower than light. Timing an echo lets you measure a distance you cannot reach — but the sound makes the journey twice, so halve your answer.