Dimensional Analysis AssistanceWatch
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).
My thought process so far is as follows:-
Looking at the original problem I can see we have
So writing the relation with assumed powers and arbritary constant
u=K p^a r^b g^c
Taking these to be proportional and subbing in dimensions I get
LT^-1 = [ML^-1T^-2]^a [ML^-3]^b [ML-2]^c
LT^-1= M^a+b+c L^-a-3b-2c T^-2a
So working out a, b c
A+b+c = 0
-a-3b-2c = 1
-2a = - 1
But I come unstuck here, am I on the right track or am I barking up the wrong tree entirely?
Apologies will repost correctly!