Solved Examples of Frequency and Period Calculations

📚 Quick Study Guide

• ⏱️ Frequency ($f$): Number of cycles per unit time. Measured in Hertz (Hz). Formula: $f = \frac{1}{T}$, where $T$ is the period.
• ⏳ Period ($T$): Time taken for one complete cycle. Measured in seconds (s). Formula: $T = \frac{1}{f}$, where $f$ is the frequency.
• 🌊 Relationship: Frequency and period are inversely proportional. Higher frequency means shorter period, and vice versa.
• 💡 Formulas for Waves: $v = f\lambda$, where $v$ is the wave speed and $\lambda$ is the wavelength.
• 🔄 Angular Frequency: $\omega = 2\pi f$, where $\omega$ is the angular frequency (rad/s).

🧪 Practice Quiz

1. A pendulum completes 20 oscillations in 10 seconds. What is its frequency?
   1. 0.5 Hz
   2. 2 Hz
   3. 10 Hz
   4. 200 Hz
2. A wave has a frequency of 5 Hz. What is its period?
   1. 0.2 s
   2. 5 s
   3. 10 s
   4. 25 s
3. If the period of a wave is 0.1 seconds, what is its frequency?
   1. 0.1 Hz
   2. 1 Hz
   3. 10 Hz
   4. 100 Hz
4. A tuning fork vibrates with a frequency of 440 Hz. What is the period of its vibration?
   1. 0.0023 s
   2. 0.023 s
   3. 2.3 s
   4. 23 s
5. A simple harmonic oscillator has a period of 2 seconds. What is its frequency?
   1. 0.5 Hz
   2. 2 Hz
   3. 4 Hz
   4. 8 Hz
6. What is the relationship between frequency and period?
   1. Directly proportional
   2. Inversely proportional
   3. Equal
   4. No relation
7. A wave travels at a speed of 10 m/s and has a frequency of 2 Hz. What is its wavelength?
   1. 2 m
   2. 5 m
   3. 12 m
   4. 20 m