Periodic Waves · 周期性波
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| wavelength/ˈweɪvleŋθ/ | 波长 | bō cháng |
Measuring a wave: how long, how tall, how often
- Keep shaking a rope steadily and you get a train of identical waves marching along.
- To describe it we measure a few key numbers — its length, its height, its rate.
- Together they obey one tidy equation linking speed, frequency and wavelength.
- Master these and you can describe any sound or light wave precisely.
测量一道波:多长、多高、多频繁
- 稳定地不断抖动一根绳,你就得到一列相同的波沿绳行进。
- 要描述它,我们测量几个关键的数——它的长度、高度、频率。
- 它们一起遵守一个简洁的方程,把速率、频率和波长联系起来。
- 掌握这些,你就能精确描述任何声波或光波。
Wavelength, amplitude, period, frequency
- Wavelength 波长 $\lambda$ — the length of one full wave (crest to crest).
- Amplitude $A$ — the height from the middle to a crest (linked to the wave's energy).
- Period $T$ — the time for one full wave to pass a point.
- Frequency $f = 1/T$ — waves per second, in hertz.
波长、振幅、周期、频率
- 波长 $\lambda$——一个完整波的长度(波峰到波峰)。
- 振幅 $A$——从中线到波峰的高度(与波的能量相关)。
- 周期 $T$——一个完整波经过某点所用的时间。
- 频率 $f = 1/T$——每秒的波数,单位赫兹。
A steady wave train · 稳定的波列
Change the frequency and watch the wavelength change while the speed stays fixed. · 改变频率并观察波长变化，而波速保持不变。
Which is the wave equation? · 哪个是波动方程？
$v = f\lambda$ — speed equals frequency times wavelength. · $v = f\lambda$ —— 波速等于频率乘以波长。
The distance from one crest to the next is the ____. · 相邻两个波峰之间的距离称为 ____。
One full wave (crest to crest) is the wavelength $\lambda$. · 一个完整波形（波峰到波峰）即为波长 $\lambda$。
The wave equation
- Speed, frequency and wavelength are linked by $v = f\lambda$.
- In one period the wave advances exactly one wavelength, so $v = \lambda / T = f\lambda$.
- If the speed is fixed (same medium), a higher frequency means a shorter wavelength.
- This single relation ties together every wave quantity.
波动方程
- 速率、频率和波长由 $v = f\lambda$ 联系。
- 在一个周期内波恰好前进一个波长,所以 $v = \lambda / T = f\lambda$。
- 若速率固定(同一介质),更高的频率意味着更短的波长。
- 这一个关系把每一个波的量联系在一起。
A wave has frequency $50\ \text{Hz}$ and wavelength $2\ \text{m}$. What is its speed, in $\tfrac{\text{m}}{\text{s}}$? · 一列波的频率为 $50\ \text{Hz}$，波长为 $2\ \text{m}$。其波速是多少，单位为 $\tfrac{\text{m}}{\text{s}}$？
$v = f\lambda = 50 \times 2 = 100\ \tfrac{\text{m}}{\text{s}}$.
At a fixed wave speed, a higher frequency means a: · 在波速固定的情况下，频率越高意味着：
$v = f\lambda$ with fixed $v$: higher $f$ gives shorter $\lambda$. · $v = f\lambda$ 固定 $v$：更高的 $f$ 导致更短的 $\lambda$。
Select all · 所有 true statements about periodic waves. · 选择关于周期性波的所有正确陈述。
$f = 1/T$, amplitude carries energy, and $v = f\lambda$. Wavelength is a length, not the height (that's amplitude). · $f = 1/T$、振幅携带能量，以及 $v = f\lambda$。波长是长度，不是高度（那是振幅）。
Reading it in sound and light
- For sound, frequency is pitch and amplitude is loudness.
- For light, frequency is colour and amplitude relates to brightness.
- A high-pitched note and blue light both have a high frequency (short wavelength).
- The wave equation applies to them all — just plug in the right speed.
在声和光中读它
- 对声,频率是音高,振幅是响度。
- 对光,频率是颜色,振幅与亮度相关。
- 高音的音符和蓝光都有高频率(短波长)。
- 波动方程对它们全都适用——只要代入正确的速率。
When a wave enters a new medium, its frequency stays the same while its speed and wavelength change. · 当波进入新介质时，频率保持不变，而波速和波长发生变化。
Frequency is set by the source and is unchanged; $v$ and $\lambda$ change together. · 频率由波源决定且不变；$v$ 和 $\lambda$ 随之共同改变。
When a wave passes into a new medium, its speed and wavelength change, but its frequency stays the same (it is fixed by the source). So use $v = f\lambda$ carefully: the frequency is the constant, and $v$ and $\lambda$ change together.
当波进入新的介质时,它的速率和波长改变,但它的频率保持不变(由波源决定)。所以用 $v = f\lambda$ 时要小心:频率是常量,而 $v$ 和 $\lambda$ 一起变化。
A wave has frequency $50\ \text{Hz}$ and wavelength $2\ \text{m}$. Find its speed.
- $v = f\lambda = 50 \times 2 = 100\ \tfrac{\text{m}}{\text{s}}$.
Double the frequency (same medium) and the wavelength halves to keep $v$ the same.
一道波频率 $50\ \text{Hz}$、波长 $2\ \text{m}$。求它的速率。
- $v = f\lambda = 50 \times 2 = 100\ \tfrac{\text{m}}{\text{s}}$。
频率加倍(同一介质),波长减半以保持 $v$ 不变。
A periodic wave is described by its wavelength $\lambda$, amplitude $A$, period $T$ and frequency $f = 1/T$. They obey the wave equation $v = f\lambda$. Entering a new medium changes $v$ and $\lambda$ but keeps $f$ fixed. For sound, $f$ is pitch; for light, $f$ is colour.
一道周期波由它的波长 $\lambda$、振幅 $A$、周期 $T$ 和频率 $f = 1/T$ 描述。它们遵守波动方程 $v = f\lambda$。进入新介质改变 $v$ 和 $\lambda$ 但保持 $f$ 不变。对声,$f$ 是音高;对光,$f$ 是颜色。