Two strings A and B, made of same material, are stretched by same tension. The r

Question

Two strings

A

and

B

, made of same material, are stretched by same tension. The radius of string

A

is double the radius of

B

. A transverse wave travels on

A

with speed

v_{A}

and on

B

with speed

v_{B}

. The ratio

(\frac{v_{A}}{v_{B}})

Options:

A . 12

B . 2

C . 14

D . 4

Answer: Option A
:
A
Two strings

A

and

B

, made of same material, are stretched by same tension. The radius of string

A

is double of the radius of

B

.A transverse wave travels on

A

with speed

v_{A}

and on

B

with speed

v_{B}

.The ratio

(\frac{v_{A}}{v_{B}})

v

\sqrt{\frac{T}{μ}}

; as

T

is constant,

v

\propto

\frac{1}{\sqrt{μ}}

But

μ

\frac{m a s s}{l e n g t h}

π r^{2} ρ

\to

μ

\propto

r^{2}

\Rightarrow

v

\propto

\frac{1}{r}

\to

\frac{v_{A}}{v_{B}}

\frac{r_{B}}{r_{A}}

\frac{r}{2 r}

\frac{1}{2}

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