Question

the density of the stretched string is changed by 2% without change in tension and radius. the change in transverse wave velocity ​

Answer 1

we know, Equation for the transverse wave velocity in a stretched string is $v=\sqrt{\frac{T}{\mu}}$

where T is tension and $\mu$ is linear mass density.

$\mu=\rho A$

where $\rho$ is density and A is cross sectional area.

now, $v=\sqrt{\frac{T}{\rho A}}$

question said tension and radius of string remain constant. so, velocity of transverse wave in a stretched string depends on density as

$v\propto\frac{1}{\sqrt{\rho}}$

to find % change in velocity, formula will be $\frac{\Delta v}{v}\times=\frac{1}{2}\frac{\Delta\rho}{\rho}\times100$

or, % change in velocity = 1/2 × % change in density

given, change in density is 2% .

so, % percentage change in velocity = 1/2 × 2 % = 1 %

Answer 2

Answer:

the above attached answer is correct correct correct