A loudspeaker produces a sound that propagates through air along the positive x-axis. At one instant an array of pressure sensors records the variation of air pressure (P−Patm) with distance x. The data are summarized verbally as follows:
• Maximum positive pressure (compression) occurs at x=0.10m,0.40m,0.70m, and so on.
• Maximum negative pressure (rarefaction) occurs halfway between successive compressions.
• Atmospheric pressure is recorded at points midway between each compression and rarefaction.
Use this description to analyze the sound wave.
(1) Part 1: (a) List the first three positions (starting at x=0) where rarefactions occur.
(2) Part 2: (b) Determine the wavelength of the sound wave.
(3) Part 3: (c) An air molecule located at x=0.25m is momentarily at atmospheric pressure. Describe the direction of its instantaneous displacement, if any, at that instant.
(4) Part 4: (d) Explain how the pressure pattern described demonstrates whether the sound wave is transverse or longitudinal.