Erratum: A multiscale analytical model of bronchial airway acoustics [J. Acoust. Soc. Am. 142, 1774–1783 (2017)]

Due to an author error (typo), Eqs. (6) and (7) are written incorrectly. Their correct forms are as follows:

$$F_v^n[\omega ]=\frac{2}{a^n\sqrt{-j{\omega \rho }_g/{\eta }_{\mathrm{g}}}}\frac{J_1\left[a^n\sqrt{-j{\omega \rho }_g/{\eta }_{\mathrm{g}}}\right]}{J_0\left[a^n\sqrt{-j{\omega \rho }_g/{\eta }_{\mathrm{g}}}\right]},$$ (6)

$$F_t^n[\omega ]=\frac{2}{a^n\sqrt{-j\omega C_g/{\kappa }_{\mathrm{g}}}}\frac{J_1\left[a^n\sqrt{-j\omega C_g/{\kappa }_{\mathrm{g}}}\right]}{J_0\left[a^n\sqrt{-j\omega C_g/{\kappa }_{\mathrm{g}}}\right]}.$$ (7)

Specifically, the Bessel function in the denominator should be to the order zero, $J_0$, not two, $J_2$, in both equations. In Eq. (6) the term in the denominator, $-j\omega {\rho }_g/{\eta }_g$, should be square-rooted, $\sqrt{-j\omega {\rho }_g/{\eta }_g}$. In Eq. (7) the term in the denominator, $-j\omega C_g/{\kappa }_g$, should be square-rooted, $\sqrt{-j\omega C_g/{\kappa }_g}$.

Due to an author error (typo), Eq. (9) was written incorrectly. The correct form is as follows:

$$Z_{w\hspace{0.17em}or\hspace{0.17em}s}^n{[\omega ]}^{\hspace{0.17em}}=R_w^n+j(I_w^n\omega -1/\omega C_w^n)\hspace{0.17em}.$$ (9)

Specifically, $I_w^n$ belongs were there was $w$.

Due to an author error, the fifth sentence of the abstract should be replaced with the following: “The fibrotic case—systemic increase in soft tissue stiffness—increased the trachea soft tissue resonance frequency.”

Due to an author error, the third sentence in the second paragraph on page 1782 is incorrect. It should be replaced by the following: “The fibrotic case, with soft tissue elastic modulus increased by a factor of 5, showed an increase by a factor of $\sqrt{5}$ from ∼115 to ∼257 Hz, of a resonance that is attributed to the trachea soft tissue resonance, denoted SgT, and determined by Eq. (15) of Lulich and Arsikere (2015). Trachea cartilage resonances did not appear in the spectrum shown in Fig. 7 due to the increased ratio of cartilage viscosity to elasticity used in this study, as compared to Lulich and Arsikere.” The cartilage elasticity used was based on the value provided in Ref. 1, which appears to be a typo, and should have been increased by an order of magnitude, which would be closer to the value used in the Lulich and Arsikere reference. With the cartilage elastic modulus increased by an order of magnitude without changing cartilage viscosity, trachea cartilage resonances do appear in the response shown in Fig. 7.