The same relation applies to longitudinal-waves of condensation reflected normally from a plane perfectly reflecting obstacle. If, however, the obstacle is not a perfect reflector some of the incident sound energy is absorbed or transmitted. Consequently the reflected-amplitude r is less than a. The expression for y now becomes in the case of perfect reflection (r= a) we obtain the ordinary expression for stationary-waves. The general expression (29) is applicable to all cases, and is represented by fig. 11. The incident energy is proportional to and the reflected energy to The reflection coefficient of the obstacle is defined as the ratio Equation (29) represents two superimposed stationary waves of maximum-amplitudes (a+r) and (a —r) respectively, and displaced r/2 in phase. Consequently the maximum and at "normal" incidence (when e1= 02= 0). If the velocity in medium (2) be greater than in medium (r), the incident waves being in the slower velocity medium, there will be a critical angle of incidence which, if exceeded, will result in total reflection.
As an example, let air and water be the media (r) and (2), sound waves being incident normally on the surface of the water. Equation (27) which expresses the reflection-amplitude in terms of the radiation impedances pc (= 111
Reflection of Plane Waves from a Plate of Finite Thickness.—This case is analogous to the optical example of reflection from a thick plate of glass—the reflected wave being the resultant of multiple reflections at the two bounding surfaces. The ratio of reflected
and incident amplitudes for normal incidence now becomes This expression for the reflection coefficient, in terms of the ratio min./max. amplitude in the stationary-wave, serves as a basis for experimental methods of measuring the reflecting properties of materials and, of course, their absorption or transmission properties. The absorption coefficient (which is generally as sumed to include transmission) is given by materials was developed by Tuma (1902), Weisbach (1910) and Hawley Taylor (1913). More recently Paris (Roy. Soc., 1927 and Phys. Soc. Proc., 1927) has refined the experimental procedure by using the hot-wire microphone to obtain accu rate values of the ratio fija, and consequently of the reflection and absorption coefficients. The plane stationary-waves were produced in a tube closed at one end by the reflector under test. The absorption coefficient was found to increase with increasing thickness of the absorber (e.g., felt) and with in crease in the frequency of the sound. Such measurements have an important application in the acoustics of buildings q.v. Stationary waves may readily be demonstrated when a high pitched sound, from a bird call or Galton's whistle, is reflected normally from a plane solid obstacle. A sensitive flame flares at all points in the path of the wave except at the nodes.