The velocity of transverse waves along a string may depend upon the length l of the string, tension F in - Physics - Waves

Question

The velocity of transverse waves along a string may depend upon the
length l of the string, tension F in the string and mass
per unit length m of the string Derive a possible formula
for the velocity dimensionally

Pintu B. · Accepted Answer

Dear Student ,

k= constant (as v is directly proportional to
l,F&m)

v=k * la

* Fb*
mc

v= k * [L]a*[M
L T-2]b

* [ML-1]c

V= k *[La]*[MbLbT-2

b]
* [McL-
c]

v= k* [Mb+c

La
+ b - c 
T-
2 b]

-2 b = -1 (1)

so, b=1/2

b+c = 0 (2)

1/2 + c =0

so, c = -1/2

a+ b- c=1 (3)

a + 1/2 - (-1/2) = 1

a+1/2+1/2 =1

a+2/2=1

a=0

so,as

v = k * la

* Fb

* mc

so, the equation formed=

v = k* l0 
* F1/2*
m-1/2

v = k (F/m)1/2

Regards

The velocity of transverse waves along a string may depend upon the length l of the string, tension F in the string and mass per unit length m of the string. Derive a possible formula for the velocity dimensionally.