(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

One formula for measuring the speed of sound in air is:

[itex]

v=\sqrt\frac{kTg}{m}

[/itex]

v=velocity

T=temperature

g=dimensionless constant

m=average mass of an air molecule

If all units are SI, what are the units ofk?

3. The attempt at a solution

I've done a lot of Googling to first try and find formulas for the speed of sound. The most similar I've seen on Wikipedia was

with the last part of the formula being the most relevant

Cideal = ideal speed

gamma = adiabatic index

k = Boltzmann Constant

T = temperature in Kelvin

m = mass of a single molecule in kg

That makes me think that k is a placeholder for the adiabatic index or the Boltzmann Constant, but I'm not sure which (if either) it is.

1. The problem statement, all variables and given/known data

In this question, the length of a wave, λ, has dimensions L, wave speed (v) has dimensons L/T, and gravitational acceleration (g) has units of L/T². Could the following be an equation for wave speed:

2. Relevant equations

[itex]

v=\sqrt\frac{g}{λ}

[/itex]

3. The attempt at a solution

λ=L

v=D/T

g=L/T²

[itex]

D/T = \sqrt\frac{L/T²}{L}

[/itex]

[itex]

D/T=\sqrt{T²}

[/itex]

[itex]

D/T=T

[/itex]

No it could not be an equation for wave speed because it is not dimensionally proportionate.

If I didn't get these right, where did I go wrong? I feel like I got the second one right, but I'm completely clueless on the first one. Thanks in advance!

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# Homework Help: Answer Checking (Speed of Sound formula, dimensional analysis)

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