On the Radiation of Sound from an Unflanged Circular Pipe

International audienceUseful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and mathematical principles are met, like hermitian symmetry for the reflection coefficient (identical behaviour of positive and negative frequencies) and causality for the impulse response. A non causal but more accurate expression is also proposed that is suitable for frequency-domain applications. The formulae are obtained by analytical and numerical fitting to reference results from Levine & Schwinger for the unflanged case and extracted from the radiation impedance matrix given by Zorum-ski for the infinite flanged case

show abstract

“…(VII.1) and (VII.2) of Ref. [1], with a maximum deviation compatible with the value of 3% mentioned in that paper.…”

Section: Unflanged Casesupporting

confidence: 88%

“…(V.16) of Ref. [1] using the quadv function from Matlab [9]. The values obtained were compared to the asymptotic approximations given by Eqs.…”

Section: Unflanged Casementioning

confidence: 99%

Approximation formulae for the acoustic radiation impedance of a cylindrical pipe

Silva

Guillemain

Kergomard

et al. 2009

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…Following Levine and Schwinger [15], the energy transmission coefficient in the frequency limit for a flanged duct is     This function appears to provide a good approximation to the general behaviour of the far field to induct pressure ratio in the low ka limit. At these low frequencies, therefore, most of the sound is reflected back into the duct with comparatively little sound power being radiated to the far field.…”

Section: Characteristics Of the In-duct And Far Field Sound Fieldmentioning

confidence: 89%

Experimental investigation of a new two-microphone method for the determination of broadband noise radiation from ducts

2017

View full text Add to dashboard Cite

This paper experimentally investigates a new technique for measuring the modal amplitude distribution, sound power transmission and radiation, and far field directivity of the broadband noise from hard walled ducts. The innovative aspect of this method is that it only requires the measurements of the two-point complex coherence function between the acoustic pressures at two closely spaced points on the duct wall. This method is therefore very useful when direct measurements of sound power and directivity are not possible. This paper describes detailed measurements of the sound power spectrum and coherence function from a hard walled circular duct excited at one end by a diffuse sound field. The other open end is terminated within an anechoic chamber with which to measure the radiated sound field at 11 microphones distributed over a polar arc. Measurements of the complex coherence were made at the duct and used to infer the sound power spectrum and far field directivity. This paper demonstrates generally good agreement between direct measurements of sound power and directivity and those inferred from the coherence function. The method is restricted to broadband noise in large ducts in the frequency range where many modes are able to propagate and the modal amplitudes are mutually uncorrelated. Nomenclature= Duct radius = Normalised mean square mode amplitude distribution for positive and negative propagating modes = Speed of sound = Schroeder frequency = Acoustic wavenumber = Acoustic pressure = Distance along duct of measurement = In-duct microphone separation distance = Duct area = Pressure amplitude of mode *Manuscript Click here to view linked References 2 3 4 5 6 7 8

show abstract

“…The first study to describe the sound field of an unflanged duct was made by Levine and Schwinger who considered the radiation of sound from rigid cylindrical duct [1]. The reduction of noise in duct systems is generally achieved by silencers.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Sound Waves with Semi Perforated Pipe

Tiryakioglu¹

2019

acperpro

View full text Add to dashboard Cite

The paper presents analytical results of diffraction phenomena at the far field and solution of the wave equation with adequate boundary condition imposed by the pipe wall. An infinite pipe with ring source and perforated part is considered. The solution is obtained by using the Fourier transform technique in conjunction with the Wiener-Hopf method. Applying the Fourier transform technique, the boundary value problem is described by Wiener Hopf equation and then solved analytically.

show abstract

On the Radiation of Sound from an Unflanged Circular Pipe

Cited by 65 publications

References 4 publications

Approximation formulae for the acoustic radiation impedance of a cylindrical pipe

Approximation formulae for the acoustic radiation impedance of a cylindrical pipe

Experimental investigation of a new two-microphone method for the determination of broadband noise radiation from ducts

Analysis of Sound Waves with Semi Perforated Pipe

Contact Info

Product

Resources

About