A speaker is located at the left end of a tube of air. When the speaker is off, the right face of the speaker is at x = 0. When the speaker is turned on, the position of the right face of the speaker is given as a function of time by u(t) = Smax sin (-wt+4) where w= 3000s!, Smax 1.00 x 10-6m, and p = 2.0. Take the speed of sound to be 335 m/s and the ambient pressure to be 1.0 atm. The molar mass of air is 29.0 g/mol. (a) Find a function which gives the displacement of the air blobs in the tube for all x and t. Give numerical values for any symbols other than x and t appearing in this function. (b) Starting from a general relation between particle displacement and pressure deviation, derive the pressure deviation (i.e. 8P) as a function of x and t. Give numerical values for any symbols other than x and t appearing in this function. What is the maximum pressure deviation associated with the sound wave? (c) Starting from a thermodynamic relation for adiabatic processes, find the maximum change in temperature due to the passage of the sound wave. (d) Floyd, whose eardrum has an area of 50 mm, puts his ear next to the end of the tube. How much sound energy does his eardrum receive in 3.0 minutes? A speaker is located at the left end of a tube of air. When the speaker is off, the right face of the speaker is at x = 0. When the speaker is turned on, the position of the right face of the speaker is given as a function of time by u(t) = Smax sin (-wt+4) where w= 3000s!, Smax 1.00 x 10-6m, and p = 2.0. Take the speed of sound to be 335 m/s and the ambient pressure to be 1.0 atm. The molar mass of air is 29.0 g/mol. (a) Find a function which gives the displacement of the air blobs in the tube for all x and t. Give numerical values for any symbols other than x and t appearing in this function. (b) Starting from a general relation between particle displacement and pressure deviation, derive the pressure deviation (i.e. 8P) as a function of x and t. Give numerical values for any symbols other than x and t appearing in this function. What is the maximum pressure deviation associated with the sound wave? (c) Starting from a thermodynamic relation for adiabatic processes, find the maximum change in temperature due to the passage of the sound wave. (d) Floyd, whose eardrum has an area of 50 mm, puts his ear next to the end of the tube. How much sound energy does his eardrum receive in 3.0 minutes
