Understanding Wave Speed: A Simple Guide

Waves are all around us, and how fast they move can change a lot depending on what they're traveling through. Knowing why waves move at different speeds helps us understand things like how sound travels in the air and how light moves through glass.

What is a Medium?
First, let’s talk about what we mean by "medium." A medium is just the material or substance that a wave travels through. Different waves need different media. For example, sound waves can travel through air, water, or solid objects, while light waves move through empty space or clear materials. The speed of the wave depends on the properties of these media.

Factors That Affect Wave Speed

1. Density of the Medium
   The density of a medium is a big factor that affects how fast waves move. For sound waves, if the density increases, the speed can change. In gases, lighter (less dense) materials let sound travel faster. That's why sound travels quicker in helium than in normal air—helium is lighter. In solids, denser materials like steel help sound move faster compared to lighter ones like rubber.

2. Elasticity
   Elasticity tells us how well a material can return to its original shape after being stretched or squished. When it comes to waves, the more elastic a material is, the faster the wave can move through it. For example, sound travels fastest in solids because they have tightly packed particles that bounce back quickly compared to liquids and gases.

3. Temperature
   Temperature also changes how fast sound travels in gases. When it gets warmer, sound usually travels faster. This happens because warmer temperatures mean the air molecules are moving around more quickly, which helps sound waves move quicker too. We can use a simple formula to see this:

   $v = 331.5 + 0.6T$

   Here, (v) is the speed of sound, and (T) is the temperature in degrees Celsius.

4. Phase of the Medium
   The state of a substance—whether it’s a solid, liquid, or gas—affects how fast waves travel. Sound moves fastest in solids, slower in liquids, and slowest in gases. This happens because particles are packed closer together in solids, which lets them share energy more quickly.

   Speed Examples:

   • Air: ~343 m/s (at 20°C)
   • Water: ~1482 m/s
   • Steel: ~5960 m/s

5. Frequency and Wavelength
   The speed of a wave depends on frequency and wavelength too. We can use this formula:

   $v = f \lambda$

   Here, (f) is the frequency (how many waves pass in one second), and (\lambda) (lambda) is the wavelength (the distance between wave peaks). If you change the frequency, the wavelength will change while the wave speed stays the same in that medium.

6. Medium Composition
   What the medium is made of also matters. Sound travels faster in dry air than in humid air because moisture changes the density. In liquids, dissolved substances can affect how quickly waves move as well.

7. Impurities in the Medium
   If the medium has impurities, that can change how fast waves travel too. For instance, sound moves differently in pure water than in water with dirt or other particles mixed in.

8. Boundary Effects
   When waves hit boundaries (like where air meets water), their speed can change. For example, sound moves faster in water than in air. This shift can also cause waves to bend, a phenomenon known as refraction.

9. Compression and Rarefaction
   Waves move by creating areas of high and low pressure, called compressions and rarefactions. This pattern helps energy move through different materials.

Conclusion

The speed of waves depends on many things like density, elasticity, temperature, phase of matter, and what the medium is made of. Understanding these factors is important for many fields, from music to technology like fiber optics. Each discovery about how waves behave helps us learn more about the world we live in and why things work the way they do.