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, its

length l and its mass m, and is given by

 where x, y, z are unknown numbers and k is

a constant. Find the values of x, y, and z.

Answer 1

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

$$LT ^ {−1} =(MLT ^{ −2} ) ^ x (L) ^ y (M) ^ z$$ $$−1=−2x→x=\frac{1}{2}\\1= \frac{1}{2} ​ +y→y=\frac{1}{2}\\0= \frac{1}{2} ​ +z→z=-\frac{1}{2}$$