1. The speed of sound in air, V B is given by the square root of the ratio of the bulk modulus B to the mass density p. Assuming ideal gas behavior, for sound waves in the andible range. the bulk modulus. dP B=-V dV is enhanced by the "adiabatic exponent" y mostly N2 and O2). = 7/5 for a diatomic gas (air is (a) Obtain expressions for B and p and from the ideal gas law, and show that the speed of sound in air increases as the square root of the ratio of the temperature T (in Kelvin) to the molecular weight Mo (in kg per mole). RT V Mo Substitute the average molecular weight for air (80% N2 and 20% O2) and calcu late the speed of sound at room temperature (70 F = 294 K). Compare your re- sult to the national weather service calculator: https://www.weather.gov/epz/wxcale_speedofsound. (b) The room temperature speed of sound in a diatomic gas composed of a single element is measured to be 220 m/s. What is the molecular weight? Use the periodic table to find the element.