In this article, acoustic properties of fibrous structures made of banana fibres have been studied. Impedance tube method was used for the testing of acoustic barrier properties. An attempt to counter low-frequency noise as well as enhancing transmission loss characteristics of fibrous structures was carried out. The effect of different parameters and arrangement of structures with respect to sound source on sound absorption as well as sound insulation of these structures has been reported. A unique structure has been developed with varying compactness throughout its thickness, and it was observed that the areal density of samples, compactness of structure and arrangement of structures can be utilised to customise its sound barrier and absorption behaviour. Maximum noise reduction coefficient of 0.78 and transmission loss up to 23 dB was observed for samples with gradient in compactness. Acoustic performance of the structure developed as a part of this research is at par or better than acoustic materials reported in literature and other commercial products.