It is important to understand that the two traveling waves in a digital waveguide are now components of a more general acoustic vibration. The physical wave vibration is obtained by summing the left- and right-going traveling waves. A traveling wave by itself in one of the delay lines is no longer regarded as ``physical'' unless the signal in the opposite-going delay line is zero. Traveling waves are efficient for simulation, but they are not easily estimated from real-world measurements , except when the traveling-wave component in one direction can be arranged to be zero.
Note that traveling-wave components are not necessarily unique. For example, we can add a constant to the right-going wave and subtract the same constant from the left-going wave without altering the (physical) sum . However, as derived in Appendix C (§C.3.6), 1D traveling-wave components are uniquely specified by two linearly independent physical variables along the waveguide, such as position and velocity (vibrating strings) or pressure and velocity (acoustic tubes).