Section outline

  • A child’s hand holds a Slinky, casting a shadow on the wall.

    Playing with a Slinky is a childhood tradition, but few children realize they are actually playing with physics .
    ::玩Slinky是童年的传统, 但很少有儿童意识到他们实际上在玩物理。

    Longitudinal Waves
    ::纵向波浪

    Like transverse waves, longitudinal waves  are mechanical waves, which means they transfer through a medium . Unlike transverse waves, longitudinal waves cause the particles of medium to move parallel to the direction of the wave. They are most common in , where they are caused by the pushing an pulling of the spring. 
    ::与反波一样,纵向波也是机械波,这意味着它们通过介质转移。 与反波不同,纵向波导致介质微粒与波向平行移动。 它们最常见于egg , 它们是由弹簧推动造成的。

    As shown in the image below, longitudinal waves are a series of compressions and rarefactions , or expansions. The of longitudinal waves is measured by the separating the densest compressions. The amplitude of longitudinal waves is the difference in media density between the undisturbed density to the highest density in a compression.
    ::如下图所示, 纵向波是一系列压缩和稀有动作, 或扩张。 纵向波是通过将最稠密的压缩分开来测量的。 纵向波的振幅是未扰动的密度与压缩中最高密度之间的介质密度差异。

      Longitudinal Waves, Showing Energy Movement And Particle Motion Directions.

    Examples
    ::实例

    Example 1  
    ::例1

    A sonar signal (sonar is traveling through water) of  @$\begin{align*}1.00 \times 10^6\end{align*}@$ Hz frequency has a wavelength of 1.50 mm in water.  What is the in water?
    ::声纳信号( 声纳正在水中运行) @$\ begin{ align} 1. 00\ times 10\\ 6\ end{ leign\ $ Hz 频率在水中波长为 1. 50 毫米。 水中是什么?

      @$\begin{align*}v=\lambda f =(0.00150 \ \text{m})(1.00 \times 10^6 \ \text{s}^{-1})=1500 \ \text{m/s}\end{align*}@$
    ::@ $\ begin{ ligin{ v lambda f = (0.00150\\ text{m} (1. 00\times 10_ 6\\ text{s} - 1})\ 1500\\ text{ m/\\\ end{ end{ ALign} = 1500\\\ text{ send{ end{ align} $

    Example 2  
    ::例2

    A of wavelength 0.70 m and 330 m/s is produced for 0.50 s.
    ::0.50秒生产波长0.70米和330米/秒的波长。

    1. What is the frequency of the wave?
      ::波浪的频率是多少?
    2. How many complete waves are emitted in this time interval?
      ::在这段时间间隔内排放了多少个完整的波?
    3. After 0.50 s, how far is the wave front from the source of the sound?
      ::0.50秒后,波前距离声音源有多远?

     

    1. @$\begin{align*}f=\frac{v}{\lambda}=\frac{330 \ \text{m/s}}{0.70 \ \text{m}}=470 \ \text{s}^{-1}\end{align*}@$
      ::@ $\ begin{ legin} legin}\ f\\\ f@ frac{ v- lumbda} frac{ 330\\\ text{ m/ s\\\\ 0.70\\ text{ m\\\\ 470\\ text{ s\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
    2. @$\begin{align*}\text{complete waves} = (470 \ \text{cycles/s})(0.50 \ \text{s}) = 235 \ \text{cycles}\end{align*}@$
      ::@ $\ begin{ align{ text{ 完整波浪} = (470\\ text{ cycles/ s} (0. 50\\ text{s}) = 235\\ text{ text{ end{ end{ align} = (470\ text{ cycolunts/ s} (0. 5\\\ text{s}) = 235\\ text{ text{ end{ end{ leign} =$
    3. @$\begin{align*}\text{distance} = (330 \ \text{m/s})(0.50 \ \text{s}) = 165 \ \text{m}\end{align*}@$
      ::@ $\ begin{ align{ text{ 距离} = (330\\ text{ m/ s} (0. 50\\\ text{s}) = 165\ text{m} end{ align$} (330\\ text{m/ s} (0. 5\\\ text{s}) = 165\\ text{ m{end{ end{ align$} =

     

    A pan flute is a musical instrument that utilizes different length tubes to produce different notes. What happens inside the flute to produce these sounds? To understand the operation of a pan flute, we need to visualize the movement of invisible air molecules inside a tube - and that isn’t easy! Launch the Pan Flute simulation below to visualize the longitudinal waves created by the movement of air in a tube:
    ::泛长笛是一种乐器,它利用不同长度的管子产生不同的音符。 长笛内会发生什么来产生这些声音? 要理解泛长笛的操作方式,我们需要将无形的空气分子在管内移动的视觉化 — — 这并不容易! 在下面启动泛长笛模拟, 以直观气管内空气运动所创造的纵向波:

    Further Reading
    ::继续阅读

    Summary
    ::摘要

    • Longitudinal waves cause the particles of medium to move parallel to the direction of the wave.
      ::纵向波导致介质微粒与波向平行移动。

    Review
    ::回顾

    1. Bats use sound echoes to navigate and hunt.  They emit pulses of high frequency sound waves which reflect off obstacles in the surroundings.  By detecting the time delay between the emission and return of a pulse, a bat can determine the location of the object.  What is the time delay between the sending and return of a pulse from an object located 12.5 m away?  The approximate speed of sound is 340 m/s.
      ::蝙蝠使用声音回声来导航和捕猎。 它们发出高频声波的脉冲, 反射周围的障碍物。 通过探测脉冲发射和返回之间的时间间隔, 蝙蝠可以确定物体的位置。 从距离12.5米的物体发送和返回脉冲之间的时间间隔是多少? 声音的大约速度是340米/秒。
    2. Sachi is listening to her favorite radio station which broadcasts radio signals with a frequency of @$\begin{align*}1.023 \times 10^8 \ \text{Hz}\end{align*}@$ .  If the speed of the signals in air is @$\begin{align*}2.997 \times 10^8 \ \text{m/s}\end{align*}@$ , what is the wavelength of these radio signals?
      ::Sachi正在收听她最喜爱的电台, 电台以@$\ begin{ align} 1.023\ times 10_8\\\ text{Hz\\\end{ align}$的频率广播无线电信号。 如果空中信号的速度是 @$\ begin{ align}\2. 997\ times 10_8\\\ text{m/ end{ leign}$, 这些无线电信号的波长是多少?
    3. A longitudinal wave is observed to be moving along a slinky.  Adjacent crests are 2.4 m apart.  Exactly 6 crests are observed to move past a given point in 9.1 s.  Determine the wavelength, frequency, and speed of this wave.
      ::观察到的纵向波浪沿着斜线移动。相近的顶峰相隔2.4米。精确的6个顶峰在9.1 s. 确定该波浪的波长、频率和速度。
    4. A sonar signal leaves a submarine, travels through the water to another submarine and reflects back to the original submarine in 4.00 s.  If the frequency of the signal was 512 cycles per second and the wavelength of the signal was 2.93 m, how far away is the second submarine?
      ::声纳信号离开潜水艇,穿过水面到另一艘潜水艇,然后在4点反射回原潜艇。如果信号的频率是每秒512个周期,信号波长为2.93米,第二艘潜艇距离多远?

    Explore More
    ::探索更多

    Use this resource to answer the questions that follow.
    ::使用此资源回答下面的问题 。

    1. In your own words, how are compressions and rarefactions produced by the tuning fork?
      ::用你自己的话来说, 调制叉子产生的压缩和稀有动作如何?
    2. Make a guess why sound can easily travel around corners (Hint: think of its medium).
      ::猜一猜为什么声音可以轻易地绕过角落(提示:想想它的介质) 。