# New PDF release: Akustik I / Acoustics I

By Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

ISBN-10: 3642459560

ISBN-13: 9783642459566

ISBN-10: 3642459587

ISBN-13: 9783642459580

**Read Online or Download Akustik I / Acoustics I PDF**

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**Additional info for Akustik I / Acoustics I**

**Example text**

T = ax (sin * - sin {} cos rp) - ay sin {} sin rp. This result is to be compared with Eq. 2) for the scattering from irregularicannot be distinties in surface impedance. 2)J, but the dipole part of the roughness scattering, dependent on LI, has a different dependence on the angles of incidence and of scattering. In addition to the usual factor r, cos cj> cos{} (cos cj> + P) (cos {} + P) there is a factor proportional to (us· k s) where Us is the velocity of the air at the surface. From here on the calculation of the scattering of sound from an area of "fine-grained roughness" can be carried out analogously to that for admittance variations discussed in the previous section. *

If the duct is driven from one end, the surface z = 0 having a z component of velocity Vk(X, y) e- iwt and the end at z-+ 00 being open, then the magnitudes Am of Eq. %-iwt -m~J~~~m II vk4>m dxd y] 4>m(X, y) e-Km%-iwt. = ~J:meL I (23·6) If the surface impedance of the sides of the duct has no real part then all the partial waves for m~mo are propagated clear to z-+ 00, but all the modes for m> mo are rapidly attenuated and are not present as z-+ 00. ) - iw, (wm=c/l-m) (23·7) is where u(x) =0 (x

Larger than e, the sound velocity in free space. , the more partial waves are propagated. Alternatively, for the m-th partial wave there is a cut-off frequency (w m/2n) = (Pm e/2n) , above which the wave is propagated, below which it dies out exponentially. When the duct wall impedance is not purely reactive, but has a resistive component, then all the eigenvalues P;' will have imaginary components, in which case all the propagation constants k m will be complex, not just those for m> mo, and thus all the partial waves are attenuated.

### Akustik I / Acoustics I by Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

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