Solved Examples: Calculating Wave Speed

📚 Quick Study Guide

• 🌊 Wave speed ($v$) is the distance a wave travels per unit time.
• 📏 The formula for wave speed is: $v = f \lambda$, where $v$ is the wave speed, $f$ is the frequency, and $\lambda$ is the wavelength.
• ⏱️ Frequency ($f$) is the number of waves that pass a point per unit time, usually measured in Hertz (Hz).
• 📏 Wavelength ($\lambda$) is the distance between two consecutive crests or troughs of a wave, usually measured in meters (m).
• 🔄 Period ($T$) is the time it takes for one complete wave to pass a point. The relationship between frequency and period is: $f = \frac{1}{T}$.
• 📢 In different mediums, wave speed can vary. For example, sound travels faster in solids than in gases.
• 💡 Remember to use consistent units when calculating wave speed!

🧪 Practice Quiz

1. A wave has a frequency of 5 Hz and a wavelength of 2 meters. What is its speed?

   1. 10 m/s
   2. 2.5 m/s
   3. 7 m/s
   4. 0.4 m/s

2. A sound wave travels at 340 m/s and has a frequency of 85 Hz. What is its wavelength?

   1. 4 m
   2. 0.25 m
   3. 255 m
   4. 425 m

3. A water wave has a wavelength of 3 meters and a period of 6 seconds. What is its speed?

   1. 0.5 m/s
   2. 2 m/s
   3. 18 m/s
   4. 9 m/s

4. If a wave has a speed of 20 m/s and a wavelength of 4 meters, what is its frequency?

   1. 5 Hz
   2. 80 Hz
   3. 16 Hz
   4. 0.2 Hz

5. A wave completes one cycle in 0.2 seconds and has a wavelength of 1.5 meters. What is its speed?

   1. 7.5 m/s
   2. 3 m/s
   3. 0.3 m/s
   4. 1.3 m/s

6. What happens to the speed of a wave if its frequency doubles and its wavelength is halved?

   1. The speed remains the same.
   2. The speed doubles.
   3. The speed is halved.
   4. The speed quadruples.

7. A wave travels 40 meters in 8 seconds. What is its speed?

   1. 5 m/s
   2. 320 m/s
   3. 0.2 m/s
   4. 48 m/s