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dtfw
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- Homework Statement
- You are testing a prototype loudspeaker for your Audio division, which may possibly be used in smoke-filled environments when nuclear reactor emergencies occur. A senior colleague has asked you to use dimensional analysis to predict how the speed of sound (u) in a gas may be influenced by the gas pressure (p), gas density (r) and acceleration due to gravity (g).
- Relevant Equations
- u=LT^-1
p=MLT^-2/L2
r=ML^-3
g=LT^-2
u=prg
LT^-1 = MLT^-2 ML^-3 LT^-2 = (ML^-2T^-2)^a (ML^-3)^b (LT^-2)c
L^2
LT^-1 = M^a L^-2a T^-2a M^b L^-3b L^c T^-2c
=M^(a+b) L^(-2a+3b+c) T(-2a+2c)
M; a+b=0
L;-2a+3b+c=1 + T^-1
Either the formula is mixed up or my method because there seem to be more unknown quantities for me to work anything out, please advise
LT^-1 = MLT^-2 ML^-3 LT^-2 = (ML^-2T^-2)^a (ML^-3)^b (LT^-2)c
L^2
LT^-1 = M^a L^-2a T^-2a M^b L^-3b L^c T^-2c
=M^(a+b) L^(-2a+3b+c) T(-2a+2c)
M; a+b=0
L;-2a+3b+c=1 + T^-1
Either the formula is mixed up or my method because there seem to be more unknown quantities for me to work anything out, please advise