Question

The velocity v of the wave set up by plucking a stretched string is found to depend on the tension T in the string, it’s length l and it’s mass m, and is given by v=kt^xl^ym^z where x,y,z are unknown numbers and k is a constant. Find the value of x, y, z

Answer 1

$$(\dim v)=(\dim t)^x(\dim l)^y(\dim m)^z$$

$$(LT^{-1})=(MLT^{-2})^x(L)^y(M)^z$$

$$-1=-2x\to x=\frac{1}{2}$$

$$1=\frac{1}{2}+y\to y=\frac{1}{2}$$

$$0=\frac{1}{2}+z\to z=-\frac{1}{2}$$