Physics 4060, Acoustics Laboratory

This lab is designed to make sure the student has some exposure to the basic classes of resonant acoustic systems. A resonant frequency is defined as a natural frequency of vibration determined by the physical properties of the vibrating object. The following experimental tests involve measuring the resonant frequency, or using the known resonant frequency to determine some other property.

本实验旨在让学生对基本的共振声学系统有所了解。共振频率定义为由振动物体的物理性质决定的自然振动频率。以下实验测试涉及测量共振频率，或利用已知的共振频率来确定其他性质。

The vibrating string is the basic example of the "standing wave" type of resonance. You should be aware that elastic waves travel up and down the string according to the basic wave relationship v = fl where v=velocity, f=frequency in Hz, and l=wavelength. The fixed ends of the string are constrained to be nodes, so the condition for resonance is

振动的弦是“驻波”类型共振的基本例子。你应该注意，弹性波根据基本的波关系式v = f l在弦上上下传播，其中v=速度，f=频率（单位为Hz），l=波长。弦的固定端被约束为节点，因此共振的条件是

where L is the string length and n is any integer, i.e., the string produces a fundamental frequency (n=1) and all harmonics of that frequency.

其中L是弦的长度，n是任意整数，即该弦产生基频（n=1）及其所有谐波。

For this part of the experiment, a metal string mounted on a wooden box called a sonometer will be used. Hang a sufficient amount of mass on the hanger to stretch the string to a reasonable tightness for producing a tone when plucked. Adjust the string supports for a convenient length of string. Hang a mass of 2 kg on the string and set up a microphone to pick up the sound of the string.

对于本实验部分，将使用安装在木盒上的金属弦，该木盒称为声学尺。挂上足够的质量以使弦绷紧到足以在拨动时发出音调的程度。调整弦的支撑点以获得方便的弦长。在弦上挂2kg的质量，并设置麦克风以接收弦的振动声。

Find the fundamental resonant frequency of the string and record it. Use this frequency and the tension to calculate the mass per unit length of the string. Predict the frequency for a 3 kg suspended to tension the string and measure it for confirmation. Calculate the tension required to tune the string to C and measure it for comparison to the expected pitch.

找出弦的基频共振频率并记录下来。利用这个频率和张力计算弦的单位长度质量。预测当3 kg重物悬挂使弦张紧时的频率，并进行测量以确认。计算将弦调至C音所需的张力，并将其与预期的音调进行比较。

B. 闭合圆柱形空气柱

Using the standard resonance tube apparatus with adjustable water level and a 440 Hz tuning fork, locate the fundamental and third harmonic resonances of the closed cylinder. Determine the speed of sound in the air in the tube. Note that the difference between the two resonant lengths should give the best wavelength determination since an end correction of about 0.6 x the radius of the tube must be applied at the open end if it is to be included in the measurement. Calculate the sound speed in m/sec and compare with the standard calculation of sound speed

使用标准的共振管装置，该装置具有可调节的水位和一个440 Hz的音叉，确定封闭圆柱体的基频和第三共振。确定管中空气的声速。注意，两个共振长度的差应给出最佳的波长测定，因为如果要将端部修正包括在测量中，开口端的修正大约为管径的0.6倍。计算声速并将其与标准计算的声速进行比较。

C. 开放圆柱（瑞基管）

You will be provided with metal tubes which have a piece of copper gauze inserted in one end of the tube to a distance about one-fifth of the tube length. Hold the tube vertically over a bunsen burner flame so that the flame will heat the gauze to red heat. After holding the end of the tube over the flame for a few seconds, you can move it to one side and you should be able to hear the pipe sound its fundamental frequency. Using the microphone and a frequency counter, measure the frequency of the sound produced. If the sound is not strong enough to measure this way, you may have to use a storage scope for the frequency determination.

您将获得一些金属管，其中一端插入了一段铜纱，其长度约为管子长度的五分之一。将管子垂直放置在酒精灯火焰上方，使火焰加热铜纱至红热状态。在将管子末端置于火焰上几秒钟后，您可以将管子移至一侧，应该能够听到管子发出的基频声音。使用麦克风和频率计，测量所产生的声音频率。如果声音不够强，无法通过这种方式测量，可能需要使用存储示波器进行频率测定。

Compare the resonant frequency to the calculated resonant frequency at room temperature, including 0.6 x radius as an end correction for the length of the tube on each end. Assuming that the standard resonant frequency calculation is valid, calculate the effective temperature (Celsius) inside the tube when it is sounding.

将共振频率与在室温下计算的共振频率进行比较，包括将管子两端各0.6倍半径作为端部修正，以修正管长。假设标准的共振频率计算是有效的，计算管内有效温度（摄氏度）。

D. 金属中声音的速率

Use the Kundt's tube apparatus to determine the velocity of sound in the metal rod. Instructions for the apparatus will be given, along with tips for the proper appreciation of its unique musical quality (bring ear plugs).

使用 Kundt 管装置测定金属棒中声速。将给出装置的使用说明，以及如何正确欣赏其独特的音色（建议佩戴耳塞）。

Stroking the metal rod with a rosin-coated cloth or skin produces longitudional waves in the rod. The vibrations of the small disc on the end of the rod produce sound waves in the air inside the glass tube, causing periodic ripple patterns in the cork dust in the tube. You will need to measure the wavelength of sound in the air, keeping in mind that the striated cork dust patterns represent antinodes and that the difference between successive antinodes is a half wavelength. You will need to measure the rod length to determine the wavelength of sound in the rod. The rod must be clamped precisely at its midpoint to vibrate properly. The rod may then be presumed to be vibrating in its fundamental longitudional mode (length = half wavelength).

用涂有罗sin的布或皮肤轻擦金属棒，会在棒中产生纵波。棒末端小盘的振动会在玻璃管内的空气中产生声波，使管中的软木粉形成周期性波纹图案。你需要测量空气中声波的波长，注意软木粉的条纹图案代表波腹，相邻波腹之间的距离为半波长。你还需要测量棒的长度以确定棒中声波的波长。棒必须精确地在中点处夹紧以正常振动。棒随后可被假设在其基本纵波模式下振动（长度等于半波长）。

To diminish the effect of end errors in the measurement of the wavelength in air, measure the overall length of as many patterns as possible and divide by the number of spaces to get a number for the half wavelength. Use the velocity of sound in air to determine the frequency of the sound.

为减少空气中波长测量中的端部误差，尽可能测量尽可能多的图案的总长度，并将总长度除以空间数目以得到半波长的数值。利用空气中声速确定声波的频率。

Use the microphone and storage oscilloscope to get a frequency for the sound and compare it with the frequency you obtained from your wavelength measurement. Compare your speed of sound in the metal with a handbook value for that metal.

使用麦克风和存储示波器获取声音的频率，并将其与你通过波长测量得到的频率进行比较。将你测得的金属中的声速与该金属的手册值进行比较。

空气腔的共振（亥姆霍兹共振）

Air cavities exhibit a single resonant frequency called a Helmholtz resonance. Such resonances are important for enhancing the tone of guitars, violins, and other string instruments. They are the absorbing frequencies of cavity type "bass traps" in studios. Tunable Helmholtz resonant cavities are used in bass-reflex type loudspeakers to enhance acoustic power and bass response (the ports you see on some loudspeakers are the openings to the Helmholtz resonators).

空气腔体表现出一个称为赫兹共振的单一共振频率。这种共振对于增强吉他、小提琴和其他弦乐器的音色非常重要。它们是录音室中称为“低音陷阱”的腔体吸收频率。可调的赫兹共振腔体被用于低音反射式扬声器中，以增强声学功率和低音响应（你可以在一些扬声器上看到的开口就是通向赫兹共振器的开口）。

In this part of the experiment, you will use a carefully designed acoustic cavity which has been shown to exhibit a prominant Helmholtz resonance (an empty Coke bottle). Blow over the end and measure the resonant frequency. Using a graduated cylinder, add 50 cm³ of water to the bottle and remeasure the frequency. Continue this process until you have filled the bottle, recording the frequency and volume of water added. Once you have filled the bottle to determine its volume, you can calculate the air volume corresponding to each of your measured frequencies. Plot the frequency as a function of the inverse square root of the air volume .

在本实验部分，你将使用一个精心设计的声学腔体，该腔体已被证明会表现出显著的共振（一个空的可乐瓶）。将瓶口吹气并测量共振频率。使用量筒，向瓶中加入50立方厘米的水，并重新测量频率。继续这一过程，直到将瓶装满，记录每次测量的频率和加入的水的体积。一旦确定了瓶的体积，就可以计算每个测量频率对应的空气体积。将频率作为空气体积倒数平方根的函数进行作图。

Measure the area of the opening (the mouth of the coke bottle) and calculate an effective neck length from the relationship above. You can use an average value for the quantity

from your data.

测量开口（煤油瓶的嘴）的面积，并根据上述关系计算出一个有效颈部长度。你可以使用你数据中的平均值来表示该量。

Overview of Resonant Systems

Physics 4060- Acoustics Laboratory

Physics 4060 Laboratory