Which bottle has the highest resonant frequency? 哪个瓶子的共振频率最高？ It is reasonable to expect that the cavity resonance frequency of the larger bottle would be lower. But in this case that is not so. The larger volume does act to lower the frequency, but the other variables that influence the cavity resonant frequency are the area of the opening and the effective length of the opening port. In this case the larger glass bottle has a cavity resonance frequency of 159 Hz compared to 148 Hz for the smaller bottle. 合理地预期较大的瓶子的共振频率会更低。但在此情况下并非如此。较大的体积确实会降低频率，但影响共振频率的其他变量是开口的面积和开口端的有效长度。在这种情况下，较大的玻璃瓶的共振频率为159 Hz，而较小的瓶子为148 Hz。

The area of the opening of the larger volume is considerably larger than that for the smaller bottle. Also the effective length of the neck of the bottle is shorter. Those two factors are enough to make the frequency slightly higher for the large bottle. 较大容器的开口面积明显大于小瓶的。此外，瓶子颈部的有效长度也更短。这两个因素足以使大瓶的频率略高。

	Click square for sound. 点击正方形以播放声音。
	Small 小	Large 大

If you click both play buttons quickly enough, you can get both bottles to play briefly and can hear the beat frequency between them.

Air Volume cm3 空气体积 cm³ Frequency Hz 频率 Hz 505 150 455 160.5 405 172 355 186 305 198.5 255 217 205 249 155 295 105 360 55 526

The data for the half-liter glass coke bottle provided a reasonable fit of the model for cavity resonance which suggests that the frequency should be inversely proportional to the square root of the volume.

Air Volume cm3 空气体积 cm³ Frequency Hz 频率 Hz 930 164.5 830 173 730 182.5 630 192.5 530 207 430 233 330 264 230 305 130 377 30 519

The data for the large glass bottle is not a bad approximation for a straight line for the larger volumes, but departs drastically from the straight line for small volumes. That's not so surprising since those resonances were close to the top of the bottle and very hard to sound. It certainly didn't appear like an enclosed cavity at those last two measurements.