How Does Temperature Affect the Speed of Sound in Air?

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The speed of sound in air is influenced by temperature, with a general formula being v ≈ 331 m/s + 0.6T, where T is the temperature in degrees Celsius. Given a frequency of 700 Hz and a wavelength of 0.5 m, the speed of sound can be calculated as 350 m/s. This indicates that the assumption of a constant speed of sound at 345 m/s is incorrect for this scenario. To find the temperature of the air, one would rearrange the formula based on the calculated speed. Understanding this relationship is crucial for solving problems related to sound propagation in varying temperatures.
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A sound wave has a frequency of 700 Hz in air and a wavelength of .50m. What is the temperature of the air?

speed of sound in air = 345 m/s.

I don't even get how to go about this problem...i don't know the equation
 
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I believe the mistake you made was to assume that the spped of sound in air is 345 m/s. You can tell just based on the information you are given in the question. If the frequency is 700 Hz and the wavelength is 0.5 m, then what MUST the speed of sound be?

There is actually a formula that relates speed of sound in air with temperature. Find that and you shall find the answer you desire.
 
Yupp, remember when the air molecules are heated up, it moves faster.
 
v\approx 331\mbox{m/s}+0.6\mbox{T}

where v is the speed of sound in air, and \mbox{T} is the temperature in degrees Celsius.
 
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