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

1. Use the method of Dimensional Analysis to show that the unknown exponents in Equation (1) are l=-1/2, m=-1, and n=1/2.

2. Relevant equations

Equation (1) is [tex]\lambda = k \mu ^{l} f ^{m} T^{n}[/tex]

Where:

[tex]\lambda[/tex] is the wavelength;

f is the frequency of the sound;

T is the tension in the string;

[tex]\mu[/tex] is the mass per unit length of the string.

k is a dimensionless constant.

3. The attempt at a solution

The dimensions for the above terms should be:

[tex]\lambda = [L][/tex] (Simple enough)

[tex]f=[L] ^{-1}[/tex] (Since the frequency is the inverse of time. Is this correct?)

[tex]T=[M][L][T] ^{-2}[/tex] (Since the tension in the rope is just the force exerted on it, right?)

[tex]\mu = [M][L] ^{-1}[/tex] (Since it is the mass per unit length)

Which gives the dimensional equation as:

[tex][L]=([M] \cdot [L]^{-1}) ^{l} \cdot ([T] ^{-1}) ^{m} \cdot ([M] \cdot [L] \cdot [T]^{-2})^{n}[/tex]

Which can be used to make equations for [L], [T], and [M], respectively:

1=-1l + 1n ([L]) (i)

0=-1m - 2n ([T]) (ii)

0=1l + 1n ([M]) (iii)

And from here I don't know where to go. If I manipulate (ii) to state n in terms of m, I get n=-1/2m. But where do I go from here? I need to solve these three equations simultaneously?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Dimensional analysis to determine unknown exponents

**Physics Forums | Science Articles, Homework Help, Discussion**