Answer to Question #88695 in Molecular Physics | Thermodynamics for GC

Question

In a student laboratory exercise, the wavelength of a 36,300 Hz ultrasound wave is measured to be 0.970 cm. Find the air temperature (in K).

Answer 1

The speed of sound in the laboratory can be calculated as

$$v=l/t=lϑ$$

 

Where 

$$l=0.970 cm=0.0097 m$$

and

$$ϑ= 36300 Hz$$

Empirically the dependence of speed of sound in the air from the air temperature had been figured out to be approximated as

$$v (m/s) = 331.5 + 0.60 T(°C)$$

Where T is in degrees of Celsius

We can then do the following

$$331.5 + 0.60 T=lϑ$$

$$T=((lϑ-331.5))/0.6$$

Finally the air temperature in Kelvin can be calculated as 

$$T_K=T+273.3=((lϑ-331.5))/0.6+273.3=307.65 K$$