Question

A source emitting sound at 385.0Hz is moving toward an observer at 32.0 m/s . The air temperature is 20.3C. What is the frequency of the sound detected by the observer? 

Answer 1

Let's first find the speed of sound at air temperature of $20.3\ ^{\circ}C$:

$$v=\sqrt{\dfrac{\gamma RT}{M}},$$ $$v=\sqrt{\dfrac{1.4\cdot8.314\ \dfrac{J}{mol\cdot K}\cdot293.45\ K}{0.032\ \dfrac{kg}{mol}}}=327\ \dfrac{m}{s}.$$

Finally, we can find the frequency of the sound detected by the observer from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v}{v-v_s}),$$ $$f_o=385\ Hz\cdot(\dfrac{327\ \dfrac{m}{s}}{327\ \dfrac{m}{s}-32\ \dfrac{m}{s}})=427\ Hz.$$