The extension in a string obeying Hook's law is x . the speed of sound in the stretched string is v . if the extension in the string is increased to 1.5x , the speed of sound will be

Question

The extension in a string obeying Hook's law is x . the speed of sound in the stretched string is v . if the extension in the string is increased to 1.5x , the speed of sound will be (A) 1.22v (B) 0.61v (C) 1.50v (D) 0.75v

Tardigrade Admin · Accepted Answer

Speed of sound in a stretched string v=√(T/μ ) ldots (i) Where T is the tension and μ is mass per unit length. According to Hooke's law, F propto x T propto x ldots (i i) From Eqs. (i) and (ii) v propto √x vâ²=√1.5v=1.22 v

Q. The extension in a string obeying Hook's law is $x$ . the speed of sound in the stretched string is $v$ . if the extension in the string is increased to $1.5 x$ , the speed of sound will be

$1.22 v$

$0.61 v$

$1.50 v$

$0.75 v$

Speed of sound in a stretched string
$v = \frac{T}{μ} \dots (i)$
Where T is the tension and $μ$ is mass per unit length.
According to Hooke's law, $F \propto x$
$T \propto x \dots (ii)$
From Eqs. (i) and (ii)
$v \propto x$
$v^{'} = 1.5 v = 1.22 v$

Q. The extension in a string obeying Hook's law is x . the speed of sound in the stretched string is v . if the extension in the string is increased to 1.5x , the speed of sound will be

1.22v

0.61v

1.50v

0.75v