Question

Assuming that the frequency v of vibrating string may depend upon (1) applied load f(2) length (1) of string and (3) was per unit length of string (4( prove that u k1|v✓f\u where u=m\1

Answer 1

$\nu \propto F^al^bm^c$

$\dim F=[MLT^{-2}]$

$\dim l=[L]$

$\dim m=[ML^{-1}]$

$\dim \nu=[T^{-1}]$

$[M^0L^0T^{-1}]=[MLT^{-2}]^a[L]^b[ML^{-1}]^c=M^{a+c}L^{a+b-c}T^{-2c}\to$

$a+c=0$

$a+b-c=0$

$-2a=-1$

So, we have

$a=\frac{1}{2}$

$b=-1$

$c=-\frac{1}{2}$

$\nu \propto F^al^bm^c=\frac{1}{l}\sqrt{\frac{F}{m}}$ . Answer