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 the Kundt's tube experiment, longitudinal sound waves are produced in a metal rod, which produces them in an air column. Using the speed of sound in air and the wave relationship, 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：即粒子的运动方向与波的传播方向一致的波。在固体如金属棒中，声音可以通过纵波或横波传播。在 Kundt 管实验中，金属棒中产生纵波声波，这些声波在空气中传播。利用空气中声速和波的关系，可以确定声波的频率和金属棒中的声速。

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 l 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，l 是波长。当棒被正确敲击并振动时，振动棒上会形成驻波。由于棒在中心被固定，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。驻波的特点是交替出现最大和最小扰动点，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。