Section 8.8: Review Examples
This section revisits key concepts from Chapters 8.1 to 8.7. Students can practice solving problems on SHM, wave properties, superposition, standing waves, and sound waves.
Example 1: SHM Displacement
A mass on a spring oscillates with an amplitude of 0.2 m and a frequency of 2 Hz. Find its displacement after 0.1 s if it starts from equilibrium.
Displacement: \( x = A \sin(2 \pi f t) = 0.2 \sin(2 \pi \cdot 2 \cdot 0.1) \approx 0.2 \sin(1.256) \approx 0.198 \text{ m} \)
Example 2: Speed of a Sound Wave
A sound wave has a wavelength of 1.5 m and a frequency of 512 Hz. Calculate its speed.
\( v = f \lambda = 512 \cdot 1.5 = 768 \text{ m/s} \)
Practice Problems
- A mass oscillates with an amplitude of 0.1 m and period 0.5 s. Find its displacement at t = 0.1 s starting from equilibrium.
- A sound wave has a frequency of 340 Hz and speed 340 m/s. Find its wavelength.
- Two waves of amplitudes 0.03 m and 0.04 m interfere constructively. What is the resultant amplitude?
- A string fixed at both ends vibrates with a fundamental wavelength of 2 m. Find the speed of the wave if its frequency is 50 Hz.
- A mass on a spring has maximum velocity 0.5 m/s. If its amplitude is 0.1 m, find its angular frequency.