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  • General

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  • 波浪速度

    Person generating a wave in a rope by moving one end up and down.

    Assume that you move one end of a rope up and down just once to generate a wave in the rope. How long will take the wave to travel down the rope to the other end? It depends on the of the wave.
    ::假设你把绳子的一端向上和向下移动了一次,以便在绳子上产生波浪。要多久波浪才能从绳子下到另一端?这取决于波浪。

    The Speed of a Wave
    ::浪潮的速度

    Wave speed is the a wave travels in a given amount of time, such as the number of meters it travels per second. Wave speed (and speed in general) can be represented by the equation:
    ::波速是指波在一定时间里行走的波速,例如每秒行走的米数。波速(和一般速度)可以用方程式表示:

    Speed = @$\begin{align*}\mathrm{\frac{Distance}{Time}}\end{align*}@$

    Wave Speed, Wavelength, and Wave Frequency
    ::波浪速度、波波长和波波频率

    Wave speed is related to both and . Wavelength is the distance between two corresponding points on adjacent waves. Wave frequency is the number of waves that pass a fixed point in a given amount of time. This equation shows how the three factors are related:
    ::波速与两者相关。波长是相邻波浪上两个对应点之间的距离。 波频率是按一定时间通过固定点的波数。 此方程式显示三个因素之间的关系 :

    Speed = Wavelength x Wave Frequency

    In this equation, wavelength is measured in meters and frequency is measured in hertz (Hz), or number of waves per second. Therefore, wave speed is given in meters per second, which is the SI unit for speed.
    ::在此方程中,波长以米计,频率以赫兹(Hz)或每秒波数计量。因此,波速以每秒米计,即用于速度的SI单位。

    Q: If you increase the wavelength of a wave, does the speed of the wave increase as well?
    ::问题:如果你增加波的波长,波的速度是否也增加?

    A: Increasing the wavelength of a wave doesn’t change its speed. That’s because when wavelength increases, wave frequency decreases. As a result, the product of wavelength and wave frequency is still the same speed. 
    ::A:增加波浪的波长不会改变其速度。 这是因为当波长增加时,波的频率就会下降。 结果,波长和波频率的产物仍然相同。

    Calculating Wave Speed from Wavelength and Wave Frequency
    ::从波长和波频频率计算波浪速度

    The equation for wave speed can be used to calculate the speed of a wave when both wavelength and wave frequency are known. Consider an ocean wave with a wavelength of 3 meters and a frequency of 1 hertz. The speed of the wave is:
    ::当波长和波频都已知时,可以使用波速度方程式计算波的速度。如果海浪波长为3米,波频为1赫兹。波的速度是:

    Speed = 3 m x 1 wave/s = 3 m/s

    Q: Kim made a wave in a spring by pushing and pulling on one end. The wavelength is 0.1 m, and the wave frequency is 2 hertz. What is the speed of the wave?
    ::问题:金在春天通过推拉一端波。波长为0.1米,波频率为2赫兹。波的速度是多少?

    A: Substitute these values into the equation for speed:
    ::A: 将这些数值替换为速度方程式:

    Speed = 0.1 m x 2 waves/s = 0.2 m/s

    Calculating Wave Frequency or Wavelength from Wave Speed
    ::从波浪速度计算波波频率或波长

    The equation for wave speed (above) can be rewritten as:
    ::波速( 以上) 的方程式可以重写为 :

    Frequency = @$\begin{align*}\mathrm{\frac{Speed}{Wavelength}}\end{align*}@$ or Wavelength = @$\begin{align*}\mathrm{\frac{Speed}{Frequency}}\end{align*}@$

    Therefore, if you know the speed of a wave and either the wavelength or wave frequency, you can calculate the missing value. For example, suppose that a wave is traveling at a speed of 2 meters per second and has a wavelength of 1 meter. Then the frequency of the wave is:
    ::因此,如果您知道波的速度以及波长或波频,您可以计算缺失值。例如,假设波以每秒2米的速度移动,波长为1米。然后波的频率是:

    Frequency = @$\begin{align*}\mathrm{\frac{2m/s}{1m}}=2 \ \text{waves/s, or 2 Hz} \end{align*}@$

    Q: A wave is traveling at a speed of 2 m/s and has a frequency of 2 Hz. What is its wavelength?
    ::问题:波以2米/秒的速度移动,频率为2赫兹。波长是多少?

    A: Substitute these values into the equation for wavelength:
    ::A: 将这些值替换成波长方程:

    Wavelength = @$\begin{align*}\mathrm{\frac{2m/s}{2 waves/s}}=1 \ \text{m} \end{align*}@$

    The Medium Matters
    ::中 中 期 事项

    The speed of most waves depends on the medium , or the matter through which the waves are traveling. Generally, waves travel fastest through solids and slowest through gases. That’s because particles are closest together in solids and farthest apart in gases. When particles are farther apart, it takes longer for the of the disturbance to pass from particle to particle through the medium.
    ::大多数波浪的速度取决于介质,或波浪所经过的事项。 一般来说,波浪在固体中移动最快,气体中速度最慢。 这是因为粒子在固体中最接近,气体中距离最远。 当粒子距离更远时,干扰从粒子到粒子通过介质需要更长的时间。

    Launch the Doppler Ducks simulation below to visualize how wave speed is related to both and . Adjust the duck slider to change how quickly the duck moves through the water.  Remember that positive velocities are rightward and negative velocities are leftward. Try playing around with having the duck go faster or slower than the wave speed, or towards or away from the boat.
    ::在下面启动 Doppler ducks 模拟, 以直观地显示波速与两者的关系。 调整鸭滑块以改变鸭子在水中移动的速度。 记住正速是向右的, 负速是向左的。 尝试让鸭子走得比波速更快或更慢, 或朝向或远离船。

    Further Reading
    ::继续阅读

    Summary
    ::摘要

    • Wave speed is the distance a wave travels in a given amount of time, such as the number of meters it travels per second.
      ::波速是波在一定时间内行走的距离,例如每秒行走的米数。
    • Wave speed is related to wavelength and wave frequency by the equation: Speed = Wavelength x Frequency. This equation can be used to calculate wave speed when wavelength and frequency are known.
      ::波速与波长和波频率有关,以方程式计算: 速度 = 波长 x 频率。当波长和频率为已知时, 此方程式可用于计算波速度 。
    • The equation for wave speed can be written to solve for wavelength or frequency if the speed and the other value are known.
      ::如果知道波长或频率的速度和其他值,可以写入波速度的方程式以解析波长或频率。
    • The speed of most waves depends on the medium, or the matter through which they are traveling. Generally, waves travel fastest through solids and slowest through gases.
      ::大多数波浪的速度取决于介质或它们所穿梭的事物。 一般来说,波浪通过固体的速度最快,气体的速度最慢。

    Review
    ::回顾

    1. What is wave speed?
      ::什么是波速?
    2. What is the speed of a wave that has a wavelength of 2 m and a frequency of 1.5 Hz?
      ::波长为2米、频率为1.5赫兹的波浪的速度是多少?
    3. Calculate the frequency of a wave that is traveling at a speed of 3.0 m/s and has a wavelength of 1.2 m.
      ::计算波的频率,波以3.0米/秒的速度移动,波长为1.2米。
    4. Sound energy travels through matter in waves. Do sound waves travel faster through air or water? Explain your answer.
      ::声音能量在波浪中穿过物质。 声音波在空气或水中走得更快吗? 请解释您的答案 。