Answer to Question #160357 in Physics for shalize

Question

An air column of length 0.92 m is open at both ends and the air temperature is 16 OC.

a) Calculate the speed of sound in air.

b) If the air column is producing the 3rd resonant frequency, calculate this frequency. 

Answer 1

(a) Let's calculate the speed of sound in air:

$$v=\sqrt{\dfrac{\gamma RT}{M}},$$ $$v=\sqrt{\dfrac{1.4\cdot8.314\ \dfrac{J}{mol\cdot K}\cdot289.15\ K}{0.032\ \dfrac{kg}{mol}}}=324.3\ \dfrac{m}{s}.$$

(b) For the third harmonic, the wavelength is $3/2$ the length of air column. Then, we can find the wavelength of the wave:

$$\lambda=\dfrac{3}{2}L=\dfrac{3}{2}\cdot0.92\ m=1.38\ m.$$

Finally, we can find the frequency from the wave-speed formula:

$$v=f\lambda,$$ $$f=\dfrac{v}{\lambda}=\dfrac{324.3\ \dfrac{m}{s}}{1.38\ m}=235\ Hz.$$