How can I use the speed of sound to calculate the air temperature?

[Sabres151]

Hey guys, need some help here with a problem. I've gotten half way thru and don't know where to go next. Here's the problem:

The wavelength of a 40,000-Hz ultrasound wave is measured to be 0.868cm. Find the air temperature.

Using v = frequency(wavelength)
40,000-Hz(0.868cm) = v
v = 347 m/s

I'm not sure where to go from here? ...Thanks for any advice!

 

[Andrew Mason]

Hey guys, need some help here with a problem. I've gotten half way thru and don't know where to go next. Here's the problem:

The wavelength of a 40,000-Hz ultrasound wave is measured to be 0.868cm. Find the air temperature.

Using v = frequency(wavelength)
40,000-Hz(0.868cm) = v
v = 347 m/s

I'm not sure where to go from here? ...Thanks for any advice!

You will need to know the relationship between the speed of sound in air and temperature.

$$v = \sqrt{\gamma RT/M}$$ so

$$T = Mv^2/R$$

where M is the molar weight of the gas (28.95 grams/mole for air) and $\gamma$ is Cp/Cv = 7/5 for a diatomic gas such as air.

See this link to the http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe3.html#c2"

AM