Waves, Compressions and Rarefactions
How does the vibration of a tuning fork reach your ear across the room? Not by sending air from the fork to the ear, but by passing on a disturbance – a wave. Your textbook (page 165, Fig 8.15) shows the air in front of a tuning fork as a pattern of crowded and spread-out regions marked C and R: compressions (മർദം കൂടിയ മേഖല) and rarefactions (മർദം കുറഞ്ഞ മേഖല). This page builds that picture step by step – from a rope and a slinky to the air itself. At the end, as a “go further”, you will meet wavelength, pitch and loudness.
- Vibration, middle position and one complete vibration (page 1).
- Particles of a medium pass a push to their neighbours (page 2).
1. A wave carries energy, not the material
Tie one end of a long rope to a pole and shake the other end up and down. A hump runs along the rope to the pole. The rope itself does not go to the pole – each bit of rope only moves up and down about its middle position. What travels is the disturbance, and with it energy: the pole gets a jerk when the hump arrives. This travelling disturbance is a wave.
Watch the red ribbon: it only goes up and down, it never moves along the rope. In this wave the rope moves across (at right angles to) the direction in which the wave travels – a transverse wave. Shaking faster gives shorter waves; shaking harder gives taller waves. The waves travel at the same speed either way – the speed depends on the rope.
When the crowd at the Jawaharlal Nehru Stadium in Kaloor, Kochi, does a “Mexican wave” during a football match, each fan only stands up and sits down in their own seat – yet the wave races right round the stadium. Drop a leaf into a temple pond and throw a pebble: ripples spread out, but the leaf only bobs up and down where it is. In every wave, the disturbance travels, the medium stays.
2. Push-pull waves on a slinky
A slinky is a long, soft spring. Lay it on a table, hold one end and push and pull it along its length. A crowded group of coils runs along the slinky, followed by a stretched-out group, then another crowded group… The crowded parts are compressions, the stretched parts are rarefactions. Each coil only moves forward and back along the same line in which the wave travels – a longitudinal (push-pull) wave. Sound is this kind of wave.
Follow the red coil. In the push-pull wave it moves back and forth along the slinky, about the dashed mark – it never leaves its place. Sound in air is a push-pull wave: C = compression, R = rarefaction.
3. Sound in air: compressions and rarefactions
Air is made of particles (page 2). When a prong of a tuning fork moves out, it pushes the air particles next to it closer together – a compression, where the pressure is a little higher than normal. When the prong moves back, it leaves more room – the particles spread out into a rarefaction, where the pressure is a little lower. The fork vibrates again and again, so a train of compressions and rarefactions travels away from it. These rapid pressure variations (മർദവ്യതിയാനങ്ങൾ) are the sound wave.
The animation is slowed down hundreds of times. Pause it and check: where the particles are crowded (C) the pressure graph is above the line; where they are spread out (R) it is below. The red particle takes turns being in a C and in an R – it moves to and fro about its dashed mark, along the direction of travel. The air does not flow to the right; only the pattern does.
- A wave is a travelling disturbance that carries energy; the medium only vibrates about its place.
- Sound is a longitudinal (push-pull) wave: the particles of the medium move to and fro along the direction in which the sound travels.
- A compression, C (മർദം കൂടിയ മേഖല), is a crowded region of higher pressure; a rarefaction, R (മർദം കുറഞ്ഞ മേഖല), is a spread-out region of lower pressure.
- When these pressure variations reach the eardrum (കർണ്ണപുടം), they push and pull it, and it vibrates (page 8).
4. Go further: wavelength, pitch and loudness
These words are not in your Class 9 textbook chapter, but they help you describe sounds. Use them for understanding; you will study them properly in higher classes.
- Wavelength (symbol λ, “lambda”): the distance from one compression to the next (or from one rarefaction to the next), in metres.
- Frequency (f): how many compressions leave the source every second, in hertz (Hz) – the same as the number of vibrations per second of the source (page 1).
- Speed (v): how far the wave travels in one second. In one second, f waves each λ long leave the source, so v = f × λ.
- Pitch – how high or low (shrill or deep) a sound is – depends on the frequency: faster vibration → higher pitch. A koel's call has a higher pitch than the rumble of thunder.
- Loudness depends on the amplitude – how big the pressure variations are (how hard the source vibrates). Strike a chenda harder: the skin vibrates through a bigger distance, and the sound is louder. Loudness is measured in decibels (dB): normal talk is about 60 dB, busy traffic about 80–90 dB, a firecracker nearby 120 dB or more (approx.).
Using a speed of sound of 350 m/s in air. Raise the frequency: compressions come closer together (shorter wavelength) and the pitch is higher. Raise the amplitude: the crowding and spreading become stronger – a louder sound. The lab is silent unless you press ▶ Play tone; it then plays a soft one-second tone at the chosen frequency.
Worked example 1 · A wave on a rope
Q. Appu shakes the end of a rope 2 times every second. The waves on the rope are 1.5 m long (from one hump to the next). How fast do the waves travel along the rope?
Every second, 2 waves leave Appu's hand, and each is 1.5 m long. How far has the front of the train moved in one second?
Worked example 2 · The wavelength of a tuning fork's sound
Q. A tuning fork vibrates 350 times every second (350 Hz). The speed of sound in air is 350 m/s. Find the distance between two neighbouring compressions (the wavelength).
Rearrange v = f × λ to get λ = v ÷ f.
We hear vibrations from about 20 Hz to 20 000 Hz (approx.). With sound at 350 m/s, what wavelengths are these?
350 ÷ 20 = 17.5 m for the deepest sounds we hear, and 350 ÷ 20 000 = 0.0175 m = 1.75 cm for the shrillest.