# Question c1f88

Jan 20, 2017

We know the relation

$v = n \times \lambda$

Where
$n \to \text{frequency of wave}$

$\lambda \to \text{wave length of wave}$

$v \to \text{velicity of wave}$

Velocity of wave being constant we can say

${n}_{1} \times {\lambda}_{1} = {n}_{2} \times {\lambda}_{2.} \ldots . \left[1\right]$

Where

${n}_{1} \to \text{initial frequency}$

${\lambda}_{1} \to \text{initial wave length}$

${n}_{2} \to \text{changed frequency}$

${\lambda}_{2} \to \text{changed wave length}$

By the given condition the wave length is reduced by 50%.
So
lambda_2=50%xxlambda_1=lambda_1/2

So by relation $\left[1\right]$

${n}_{1} \times {\lambda}_{1} = {n}_{2} \times {\lambda}_{1} / 2$

$\implies {n}_{2} = 2 {n}_{1}$

Percent increase in frqyency

=(n_2-n_1)/n_1xx100%

=(2n_1-n_1)/n_1xx100%=100%#