Practice Problems

1. A mass oscillates with amplitude 0.15 m and frequency 3 Hz. Find its displacement at t = 0.05 s starting from equilibrium.
2. A string vibrates with fundamental frequency 200 Hz and wavelength 1.2 m. Find the wave speed.
3. Two waves of amplitudes 0.02 m and 0.05 m interfere destructively. Determine the resultant amplitude.
4. A mass on a spring has angular frequency 4 rad/s and amplitude 0.1 m. Find its maximum speed.
5. A tube open at both ends resonates at 340 Hz with speed of sound 340 m/s. Find the wavelength of the fundamental.
6. A mass oscillates with a period of 0.4 s. What is its frequency and angular frequency?
7. Two waves of equal amplitude 0.03 m and same frequency superpose constructively. Find the resultant amplitude.
8. A mass attached to a spring has a maximum velocity of 0.6 m/s and amplitude of 0.12 m. Find its angular frequency and period.
9. A sound wave of frequency 512 Hz and wavelength 0.66 m travels through air. Verify its speed and comment on whether it matches typical speed of sound in air.
10. A string fixed at both ends vibrates in its third harmonic at 450 Hz. Find the fundamental frequency if the string length is 1.5 m and wave speed is 150 m/s.