On the relation between the acoustic impedance and the profile of periodic travelling waves in a 1D wave equation

Key Points

• The research aims to explore the conditions for existence of travelling waves in a linear 1D wave equation with periodic acoustic impedance.
• Studied the existence of periodic travelling waves based on given acoustic impedance.
• Investigated the inverse problem to determine acoustic impedance functions that support specific travelling waves.
• Provided results on the regularity of the acoustic impedance function.
• Validated findings with numerical simulations.
• Demonstrated the existence of periodic travelling waves for specified acoustic impedance.
• Identified acoustic impedance functions that can support waves of predetermined amplitude.
• Highlighted certain regularity conditions for acoustic impedance functions required for wave existence.