﻿ 玻璃酒杯声波激振的原理及其影响因素的探讨 Discussion on Principle and Influence Factors of the Acoustic Excitation of the Wine Glasses

Applied Physics
Vol.07 No.09(2017), Article ID:22181,10 pages
10.12677/APP.2017.79035

Discussion on Principle and Influence Factors of the Acoustic Excitation of the Wine Glasses

Jiashun Yan1, Na Zhao1, Xiaofeng Zhao1*, Yuxin Zhang, Chaoyu Yu1, Yongan Lao2

1Department of Physics, Chengdu University of Technology, Chengdu Sichuan

2Department of Bioengineering, Chengdu University of Technology, Chengdu Sichuan

Received: Sep. 8th, 2017; accepted: Sep. 23rd, 2017; published: Sep. 27th, 2017

ABSTRACT

In this paper, the arm force rod model is built to illustrate the microscopic mechanism of acoustic excitation and the vibrational modes of higher order are discussed ulteriorly. Five main factors, the height of the liquid level, liquid density, viscosity, temperature and the size of the wine glasses, are analyzed through experiments. The result shows the relationship between liquid levels or its density and frequency of wine glasses are negatively correlated and their value verifies the theoretical model well. Except that, the result also shows liquid viscosity and temperature are negatively correlated with the frequency, and the sensitivity of different size of wine glass to the liquid level and temperature is different.

Keywords:Arm Force Rod Model, Vibrational Modes of Higher Order, Five Main Factors, French Energy Model

1成都理工大学物理系，四川 成都

2成都理工大学生物工程系，四川 成都

1. 引言

2. 共振的理论模型

2.1. 臂力棒模型

2.2. 共振频率的计算方法

$x\left(z,\theta ,t\right)={A}_{0}f\left(z\right)\mathrm{cos}2\theta \mathrm{cos}\omega t$ (1)

Figure 1. Diagram of the acoustic excitation of the wine glasses

Figure 2. Propagation of stress waves

Figure 3. Propagation of stress waves

Figure 4. Figure of simplified glass

Figure 5. Figure of simplified glass

Figure 6. Diagram of resonance phenomenon

${f}_{0}=\frac{1}{\text{2π}}{\left(\frac{3Y}{5{\rho }_{g}}\right)}^{\frac{1}{2}}\frac{a}{{R}^{2}}{\left[1+\frac{4}{3}{\left(\frac{R}{H}\right)}^{4}\right]}^{\frac{1}{2}}$ (2)

${\left(\frac{{f}_{0}}{{f}_{d}}\right)}^{2}\approx 1+\frac{\beta {\rho }_{l}R}{5{\rho }_{g}a}{\left(\frac{h}{H}\right)}^{4}$ (3)

${f}_{d}\approx \frac{{f}_{0}}{\sqrt{1+\frac{\beta {\rho }_{l}R}{5{\rho }_{g}a}{\left(\frac{h}{H}\right)}^{4}}}$ (4)

2.3. 多极共振模式

$A\left(\theta ,t\right)={A}_{0}\left[\mathrm{sin}\left(n\theta +{v}_{F}t\right)+\mathrm{sin}\left(n\theta -{v}_{F}t\right)\right]$ (5)

${v}_{F}={\left(\frac{\text{π}a{v}_{L}{f}_{n}}{\sqrt{3}}\right)}^{\frac{1}{2}}$ (6)

${f}_{n}=\frac{{n}^{2}a{v}_{L}}{2\text{π}{R}^{2}\sqrt{12}}$ (7)

3. 实验结果与分析

3.1. 液体高度对频率的影响

Figure 7. Figure of high-order vibration modes

Figure 8. Diagram of experimental device

· 取干净的350 ml酒杯，并倒满蒸馏水但注意不要溢出，控制水面的最高处恰好到达杯口位置；

· 调节扩音器输出音频的频率，直至在显示屏上观察到最大振幅的共振现象，并记录此时频率fd

· 测量水面高度h，并从玻璃酒杯中用针管抽取10 ml水，重复1、2步骤；

${f}_{d}=\frac{{f}_{0}}{\sqrt{1+\frac{\beta {\rho }_{l}R}{5{\rho }_{g}a}{\left(\frac{h}{H}\right)}^{4}}}$ (8)

3.2. 液体密度对频率的影响

${\left(\frac{{f}_{0}}{{f}_{d}}\right)}^{2}=1+\frac{\beta {\rho }_{l}R}{5{\rho }_{g}a}{\left(\frac{h}{H}\right)}^{4}=1+k*{\rho }_{l}$ (9)

3.3. 液体黏度系数对频率的影响

3.4. 液体黏度系数对频率的影响

3.5. 杯子尺寸对频率的影响

Figure 9. Fitting result of liquid level-frequency

4. 结论

Figure 10. Result of the first order fitting

Figure 11. Relation of liquid density-frequency

Figure 12. Relation of temperature-frequency

Figure 13. Relation of temperature-frequency of different size glasses

Figure 14. Relation of glass size-frequency

Table 1. Result of fitting data

Discussion on Principle and Influence Factors of the Acoustic Excitation of the Wine Glasses[J]. 应用物理, 2017, 07(09): 283-292. http://dx.doi.org/10.12677/APP.2017.79035

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