Newtonian mechanics, one can derive the following expression for the speed of sound in an elastic medium: vs = vb, where b is the bulk modulus, defined as b = - v. b is the change in pressure per fractional change in volume. [the inverse of the bulk modulus is called the compressibility.] a) the value of the bulk modulus depends on whether conditions are isothermal or adiabatic. compute b for an ideal gas for both isothermal and adiabatic conditions. give your answers in terms of pressure p and the constant y = 172. b) the constant y for an idea gas can be determined experimentally from the heat capacities of the gas. derive a formula for y using both cp and cv for an ideal gas. c) argue that for computing the speed of sound, it is the adiabatic b (not the isothermal b) that is the correct one to use. d) using the formula vs = vb, derive an expression for the speed of sound in air in terms of the temperature t and the average molecular mass m. compare this with the formula for the rms speed of molecules in air. compute the numerical value of the speed of sound in air at room temperature.