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Physics · 术语表

什么是 Signal; sinusoidal signal？

Definition 5.1 University Physics — Year 1 · 第 5 章 — Signal Propagation: Travelling and Standing Waves

A signal is a physical quantity that varies in time and carries information: the acoustic overpressure at a microphone, the voltage at an antenna, the transverse displacement of a point of a string. The sinusoidal signal

s(t) = A\cos(\omega t + \varphi)

has amplitude $A > 0$ , angular frequency $\omega$ ( $\mathrm{rad}/\mathrm{s}$ ), frequency $f = \omega/2\pi$ , period $T = 1/f$ and initial phase $\varphi$ ; $\omega t + \varphi$ is its phase at time $t$ .

示例

Example 5.14 (Two loudspeakers)

Two speakers $2.0\,\mathrm{m}$ apart play the same $850\,\mathrm{Hz}$ tone in phase ( $\lambda = 0.40\,\mathrm{m}$ ). On the perpendicular bisector $\delta = 0$ : loud everywhere. Along the segment joining them, $\delta$ changes by $2\lambda$ per wavelength of displacement, so quiet spots ( $\delta = \pm\lambda/2, \pm 3\lambda/2, \dots$ ) sit every $\lambda/2 = 20\,\mathrm{cm}$ — a standing wave, the subject of the next section. Move one speaker’s wire so it plays in opposite phase, and loud and quiet exchange places.

Example 5.15 (Young’s holes)

Two pinholes $S_1$ , $S_2$ a distance $a$ apart, lit by one monochromatic source (so that they emit in phase), send light to a screen at distance $D \gg a$ . At a point of the screen at height $x$ from the axis, the path difference is

\delta = S_2M - S_1M \approx \frac{a\,x}{D}

(for $x \ll D$ : $S_{1,2}M = \sqrt{D^2 + (x \mp a/2)^2} \approx D + (x \mp a/2)^2/2D$ , and subtract). Bright fringes at $x = n\lambda D/a$ : the fringe spacing is

i = \frac{\lambda D}{a} .

With $a = 0.50\,\mathrm{mm}$ , $D = 2.0\,\mathrm{m}$ , $\lambda = 633\,\mathrm{nm}$ : $i = 2.5\,\mathrm{mm}$ — a ruler measures the wavelength of light. In a medium of index $n$ the path difference to use is the optical path $n \times$ length, since $\lambda = \lambda_0/n$ .

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