The passive control of low-frequency duct noise remains a technical challenge. Herschel-Quincke (HQ) tube is effective in low frequency noise reflection. Previous studies showed that, when the bypass of the HQ tube is filled with a lighter gas and covered by tensioned membranes, the HQ tube becomes a flute-like silencer [L.Huang, Attenuation of low frequency duct noise by a flute-like silencer, Journal of Sound and Vibration 326 (2009) 161–176]. Another resonance occurs and the transmission loss spectrum can keep a desirable high level. In this paper, a two-dimensional analytical method for flute-like silencer is developed and this method offers an effective way in acoustic calculations with variable parameters. The details of the modal behavior are analyzed and a parametric study is conducted to obtain optimal design. It shows that the noise attenuation mechanism can be interpreted as destructive interference and the resonance of a single spring-mass system. The trends of the experimental results and theoretical calculations are in good agreement, however, significant deviations in absolute value are observed around the second peak of the transmission loss. Minimizing sound and gas leakage is still an issue that needs to be considered. The effects of cavity filling with different gases are also investigated and it is found that the use of hydrogen can bring performance improvement in low-frequency range. After the introduction of another stretched membrane, the optimal logarithmic bandwidth of the silencer can be further extended to about 5.2.

低频风道噪声的被动控制仍然是一项技术挑战。Herschel-Quincke（HQ）管在低频噪声反射中很有效。先前的研究表明，当HQ管的旁路充满较轻的气体并被张紧的膜覆盖时，HQ管会变成类似长笛的消音器[L. Huang，用类似长笛的消音器来降低低频管道噪音，声音与振动杂志326（2009）161-176]。发生另一个谐振，并且传输损耗频谱可以保持理想的高电平。本文提出了一种用于长笛状消声器的二维分析方法，该方法为可变参数声学计算提供了一种有效的方法。分析了模态行为的细节，并进行了参数研究以获得最佳设计。它表明，噪声衰减机制可以解释为相消干涉和单个弹簧质量系统的共振。实验结果和理论计算的趋势吻合良好，但是，在传输损耗的第二个峰值附近观察到了绝对值的显着偏差。最小化声音和气体泄漏仍然是需要考虑的问题。还研究了用不同气体填充腔体的效果，发现使用氢气可以改善低频范围内的性能。引入另一张拉伸膜后，消音器的最佳对数带宽可进一步扩展至约5.2。