Head waves from a linear transition layer in a liquid

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An approximate harmonic solution has been derived for head waves from a linear velocity transition layer in a liquid medium of uniform density. When the frequency of wave motion is much higher than the spatial gradient of velocity in the transition layer, the velocity potential decreases with increasing frequency in proportion to the minus two-thirds power of the frequency. In the frequency range approximately equal to the velocity gradient, the velocity potential is nearly constant for some frequency ranges and has a relatively sharp decrease in amplitude at the high-frequency end. This phenomenon is similar to that observed previously in plastic models.