Wave Speed As a Function of Tension

[neoking77]

Homework Statement

This is a question from my lab manual
v=Cmu^aT^b (4.3)
Use dimensional analysis of equation (4.3) to determine the exponents a and b.

Homework Equations

i know that the proper equation is
v=sqrt(T/mu)

The Attempt at a Solution

I tried dimensional to get some sort of exponent of 1/2 and -1 for mu in there...but not much luck. can anyone tell me what I'm doing wrong?

m/s = (kg/m)(kgm/s^2)
m/s = kg^2/s^2
ms = kg^2
sry...i've always been bad at dimensional analysis x_x any help would be greatly appreciated!

 

[learningphysics]

What is mu?

 

[neoking77]

sry forgot to say
mu is mass per unit length of the wire

 

[learningphysics]

sry forgot to say
mu is mass per unit length of the wire

okay, so

m/s = (kg/m)^a* (kgm/s^2)^b

and simplifying this:

m/s = kg^(a+b)*m^(b-a)*s^(-2b)

now using the exponents of kg, m and s on both sides... try to get some equations and solve for a and b.

 

[neoking77]

by using exponents on both side, do u mean to raise m/s to the power of (a+b)(b-a)(-2b)??

 

[learningphysics]

by using exponents on both side, do u mean to raise m/s to the power of (a+b)(b-a)(-2b)??

no. you need the exponents to match on both sides...

what is the exponent of kg on the left side? what is the exponent of kg on the right side?

 

[neoking77]

now i get it! thanks so much!

the ansr i got was a=-1/2 and b=1/2, which is in accordance with
v = sqrt(T/mu)

 

[learningphysics]

now i get it! thanks so much!

the ansr i got was a=-1/2 and b=1/2, which is in accordance with
v = sqrt(T/mu)

yup. Looks good!