Oscillations and Waves
Beginner
Wave function
Source: High school physics (Chinese)
Problem Sets:
Waves
Problem
A transverse wave traveling along a long string is described by
$$x = 2.0\times 10^{-3}\sin(600t - 200y) \text{ m}.$$- Find the amplitude, frequency, wave speed, and wavelength of this wave.
- Find the maximum transverse speed of a particle on the string.
(1) $A = 2.0\times10^{-3}$ m, $f \approx 95.5$ Hz, $v = 3.0$ m/s, $\lambda \approx 3.14\times10^{-2}$ m. (2) $u_{\max} = A\omega = 1.2$ m/s.
Compare with the standard form $x = A\sin(\omega t - ky)$: the amplitude is $A = 2.0\times10^{-3}$ m, the angular frequency is $\omega = 600$ rad/s, and the wave number is $k = 200$ rad/m.
(1)
$$f = \frac{\omega}{2\pi} = \frac{600}{2\pi} \approx 95.5 \text{ Hz}, \qquad \lambda = \frac{2\pi}{k} = \frac{2\pi}{200} \approx 3.14\times10^{-2} \text{ m},$$ $$v = \frac{\omega}{k} = \frac{600}{200} = 3.0 \text{ m/s}.$$(2) The transverse speed is greatest as the particle passes through equilibrium:
$$u_{\max} = A\omega = (2.0\times10^{-3})(600) = 1.2 \text{ m/s}.$$