3.1 General Properties of Waves
Wave Speed Equation
In physics, the speed of a wave (\$v\$) is the product of its frequency (\$f\$) and wavelength (\$\lambda\$):
\$v = f \lambda\$
Key Concepts
- Frequency (\$f\$) – How many wave crests pass a point each second. Measured in hertz (Hz). 🔁
- Wavelength (\$\lambda\$) – Distance between two successive crests. Measured in metres (m). 📏
- Wave speed (\$v\$) – How fast the wave travels through the medium. Measured in metres per second (m/s). 🚀
Analogy: Traffic on a Highway
Imagine cars (wave crests) moving along a highway (the medium).
- The frequency is how many cars pass a fixed point each second.
- The wavelength is the distance between two consecutive cars.
- The speed is how fast each car travels.
The relationship \$v = f \lambda\$ tells us that if cars are closer together (shorter wavelength) or if more cars pass a point each second (higher frequency), the overall speed of traffic changes accordingly.
Real‑World Examples
- Guitar string – Pull the string tighter (higher frequency) or shorten it (shorter wavelength) to change the pitch.
- Radio waves – Different stations use different frequencies; the wavelength determines how the waves travel through the atmosphere.
- Sound in air – The speed of sound is roughly 343 m/s at room temperature, independent of frequency for most audible sounds.
Units and Conversion
| Quantity | Symbol | Units |
|---|
| Frequency | \$f\$ | Hz (s⁻¹) |
| Wavelength | \$\lambda\$ | m |
| Speed | \$v\$ | m s⁻¹ |
Practice Problems
- A radio wave has a frequency of 100 MHz. If its wavelength is 3 m, what is its speed?
Answer: \$v = 100\times10^6 \, \text{Hz} \times 3 \, \text{m} = 3.0\times10^8 \, \text{m/s}\$. - A sound wave travels at 340 m/s and has a frequency of 170 Hz. Find its wavelength.
Answer: \$\lambda = \frac{v}{f} = \frac{340}{170} = 2 \, \text{m}\$. - In a guitar string experiment, the frequency is doubled while the wavelength is halved. What happens to the wave speed?
Answer: The speed remains unchanged because \$v = f \lambda\$ and the changes cancel out.
Summary
Remember: Wave speed (\$v\$) = Frequency (\$f\$) × Wavelength (\$\lambda\$).
- Increase frequency → higher speed if wavelength constant.
- Increase wavelength → higher speed if frequency constant.
- If both change proportionally, speed stays the same.
Use this formula to solve everyday wave problems, from music to radio to light.