Recall and use the equation for wave speed v = f λ

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

1. Guitar string – Pull the string tighter (higher frequency) or shorten it (shorter wavelength) to change the pitch.
2. Radio waves – Different stations use different frequencies; the wavelength determines how the waves travel through the atmosphere.
3. 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

Practice Problems

1. A radio wave has a frequency of 100 MHz. If its wavelength is 3 m, what is its speed?
   Answer: $v = 100\times10^6 \, \text{Hz} \times 3 \, \text{m} = 3.0\times10^8 \, \text{m/s}$.
2. A sound wave travels at 340 m/s and has a frequency of 170 Hz. Find its wavelength.
   Answer: $\lambda = \frac{v}{f} = \frac{340}{170} = 2 \, \text{m}$.
3. 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.