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Practice Test — Vibrations & Waves Math
Practice Test — Vibrations & Waves
Practice Test — 20 Questions
1. $x = 4\sin(8\pi t)$. Find frequency.
2. Mass-spring: $k = 100$, $m = 1$. Find $T$.
3. Pendulum: $L = 4$ m. Find $T$.
4. $A(t) = 10e^{-0.3t}$. Amplitude at $t = 5$?
5. Half-life of amplitude with $\gamma = 0.2$?
6. $v = f\lambda$. $v = 340$, $f = 680$. $\lambda$?
7. Wavelength of 100 MHz FM wave?
8. Beat frequency: 500 Hz and 503 Hz?
9. 3rd harmonic of a string with $f_1 = 150$ Hz?
10. What causes resonance?
11. $T = 2\pi\sqrt{m/k}$. Solve for $k$ if $T = 1$ s, $m = 0.25$ kg.
12. Wave speed on a string doubles. What happens to frequency (fixed $\lambda$)?
13. $x = 7\cos(\omega t)$. What is the maximum velocity?
14. Two waves add: constructive interference occurs when phase difference = ?
15. Light: $\lambda = 700$ nm. What color?
16. $f_n = n \cdot v/(2L)$. $L = 0.5$ m, $v = 200$ m/s. $f_1$?
17. Is a shock absorber underdamped or overdamped?
18. Period of a 60 Hz electrical signal?
19. $\omega = 2\pi f$. $f = 50$ Hz. $\omega$?
20. What principle says $y_{total} = y_1 + y_2$?
Show Answer Key
1. $\omega = 8\pi$, $f = 4$ Hz
2. $T = 2\pi\sqrt{1/100} = 2\pi(0.1) \approx 0.628$ s
3. $T = 2\pi\sqrt{4/9.8} \approx 4.01$ s
4. $10e^{-1.5} \approx 2.23$
5. $\ln 2/0.2 = 3.47$ s
6. 0.5 m
7. $3 \times 10^8/10^8 = 3$ m
8. 3 Hz
9. 450 Hz
10. Driving frequency matches natural frequency.
11. $k = m(2\pi/T)^2 = 0.25 \times 4\pi^2 \approx 9.87$ N/m
12. Frequency doubles.
13. $v_{max} = A\omega = 7\omega$
14. 0° (or $2n\pi$)
15. Red
16. 200 Hz
17. Critically damped or slightly overdamped (no bouncing, quick return).
18. $1/60 \approx 0.0167$ s
19. $100\pi \approx 314.2$ rad/s
20. Principle of superposition.