Longitudinal Waves - Kundt's Tube

Sound in air is propagated only by means of longitudinal waves; waves in which the particle's motion consists of oscillations back and forth in the direction of propagation. In a solid such as a metal rod, sound can be transmitted either by longitudinal or transverse waves. In this experiment, longitudinal sound waves will be produced in a metal rod and an air column. Using the properties of wave motion, the frequency of the sound and the speed of sound in the rod can be determined.

在空气中，声音只能通过纵波传播；纵波是指粒子的运动方向与波的传播方向一致的往复振荡。而在固体如金属棒中，声音可以通过纵波或横波传播。在本实验中，将在金属棒和空气柱中产生纵波。利用波的性质，可以确定声音的频率和在金属棒中的声速。

The apparatus consists of a glass tube supported on a metal base as shown in the diagram. A clamp at one end of the base holds a metal rod which has a metal disk attached to one end. The rod and disk extend inside the glass tube, whose position can be adjusted to center the tube about the disk. It is important to make sure the disk is not touching the glass becuause the vibrations set up in the rod will break the glass. A stopper closes the other end of the tube. The velocity of any wave is given by:

该装置由一个放在金属底座上的玻璃管组成，如图所示。底座一端的夹具固定着一根金属棒，其一端连接着一个金属盘。棒和盘延伸到玻璃管内，管的位置可以调节以使管围绕盘中心对齐。必须确保盘不接触玻璃管，因为棒中产生的振动会破裂玻璃。另一端用塞子封闭。任何波的速度由以下公式给出：

where f is the frequency and λ is the wavelength. When the rod is properly stroked and set into vibration, standing waves are set up in the vibrating rod. Since the rod is clamped at its center point, this point is a node (zero amplitude of motion) and the ends which are free to vibrate are antinodes (maximum amplitude of particles' motion along the direction of the rod).

其中，f 是频率，λ 是波长。当棒被正确敲击并振动时，会在振动的棒中形成驻波。由于棒在中心被夹紧，该点是一个节点（运动幅度为零），而两端可以自由振动，因此是波节（粒子沿棒的方向运动幅度最大）。

When the rod is vibrating in this manner it is vibrating with its fundamental frequency and the wavelength of the standing wave is twice the length of the rod.

当杆以这种方式振动时，它正在以基频振动，驻波的波长是杆长的两倍。

The vibrations of the rod are transmitted by the disk to the air in the glass tube closed at one end.The waves set up in the air in the glass tube have the same frequency as those in the rod. The waves are reflected at the closed end of the tube and the air in the tube is thus acted upon by two similar sets of waves travelling in opposite directions. When the length of the air column is some multiple of half wavelengths, the two oppositely travelling waves produce standing waves. The standing waves are characterized by alternate points of maximum and minimum disturbance called respectively nodes and antinodes. These nodes and antinodes may be detected by cork dust placed in the tube, the cork dust showing characteristic striated vibration patterns at the antinodes. The distance between two successive patterns is therefore one-half the wave length of the sound in the air.

杆的振动通过盘传递到玻璃管中的空气，该玻璃管一端封闭。在玻璃管中的空气形成的波具有与杆中波相同的频率。这些波在管的封闭端发生反射，因此管中的空气受到两个方向相反的波的共同作用。当空气柱的长度是半波长的整数倍时，这两个反向传播的波形成驻波。驻波的特点是交替的极大和极小扰动点，分别称为节点和腹点。这些节点和腹点可以通过在管中放置软木屑来检测，软木屑在腹点处显示出特征的条纹振动图案。因此，两个连续图案之间的距离是声波在空气中的半波长。

The wave length of the sound in air is thus determined. From tables the velocity of sound in air at the temperature of the room is obtained and using equation (1) the frequency may be computed. Since this is the frequency of the sound wave in the metal rod and since the wave length is twice the length of the rod, we can compute the velocity of the sound waves in the metal rod using equation (1).

声波在空气中的波长因此得以确定。从表中可以得到空气在室温下的声速，利用方程（1）可以计算出频率。由于这是金属棒中声波的频率，而波长是棒长的两倍，因此可以利用方程（1）计算出金属棒中声波的声速。

Procedure: Place a thin layer of very dry cork dust at least two millimeters wide as uniformly as possible inside the tube along its entire length. It is necessary that the cork dust and the glass tube be perfectly dry. Insert the stopper in the end of the tube. With the rod securely clamped at its center, position the glass tube so that the disk on the end of the rod is a few centimeters within the tube and centered with respect to the sides.

步骤：在管子的整个长度内尽可能均匀地放置一层非常干燥的松香粉，厚度至少为两毫米。松香粉和玻璃管必须完全干燥。将塞子插入管子的一端。将杆牢固地夹在中心位置，将玻璃管放置好，使杆的盘状物端面在管内约几厘米处，并且居中对齐管的两侧。

Place a small amount of the rosin on a piece of leather cloth or chamois skin. Gripping the rod with the rosined leather, pull toward the end of the rod. Try to avoid pulling the cloth completely off the rod because this sets up transverse waves in the rod and may break the glass tube. Proper stroking sets the the rod into longitudinal vibrations and a note of high pitch will be heard. This stroking of the rod usually requires a little practice to produce satisfactory vibration, but is relatively easy once the proper technique is acquired. Slide the glass tube a short distance one way or the other while continuing the stroking until the most distinct dust heaps are obtained.

在一块皮革布或鹿皮上放一点松香。握住有松香的皮革，向杆的末端拉。尽量避免把布完全从杆上拉下来，因为这会在杆上产生横向波，可能使玻璃管破裂。正确的摩擦会使杆产生纵向振动，会听到高音调的声音。这种摩擦通常需要一些练习才能产生满意的振动，但一旦掌握了正确的技巧，就相对容易了。在继续摩擦的同时，将玻璃管向一方向滑动一段距离，直到获得最明显的尘堆。

The distance between successive dust heaps is difficult to measure accurately because the exact center of the dust heap cannot be ascertained definitely. However, a good average can be obtained by measuring the distance over a large a number of dust heaps as possible and dividing by this number. Twice this value is the wave length of the sound. Record the room temperature and calculate the velocity of sound in air at this temperature:

相邻尘堆之间的距离难以准确测量，因为尘堆的确切中心无法确定。然而，可以通过测量大量尘堆之间的距离并将其除以数量来获得一个较好的平均值。这个值的两倍就是声波的波长。记录房间温度，并计算该温度下空气中声速：

Compute the frequency of the sound. Measure the length of the metal rod and using the measured frequency of the sound compute the velocity of sound in the metal rod. Compare this with handbook values for velocity of sound in this material.

计算声音的频率。测量金属棒的长度，并利用测得的频率计算金属棒中声速。将此结果与手册中该材料的声速值进行比较。

Longitudinal Waves - Kundt's Tube

Equipment: Kundt's Tube