Question

If wavelength of a sound wave in medium is reduced by 50 per cent , what will be the percentage change in its frequency​

Answer 1

The frequency  of sound wave is increased by 100%

Explanation:

Let v be the constant speed of sound

Let $\lambda$ be the initial wavelength of sound and $\nu$ be the initial frequency of sound.

We know that the relation between wavelength and frequency is given by

$v=\nu\times \lambda$

Where

$\nu$=Frequency of sound

$\lambda$=Wavelength of sound

$v$=Velocity of sound

$\nu=\frac{v}{\lambda}$.....(1)

Wavelength of sound wave is reduced by 50%

Then, the wavelength of sound wave=$(1-0.50)\lambda=0.50\lambda=\frac{1}{2}\lambda$

Frequency of sound wave =$\nu'=\frac{v}{\frac{1}{2}\lambda}$...(2)

Equation (2) divided by equation(1) then we get

$\frac{\nu'}{\nu}=\frac{\frac{v}{\frac{1}{2}\lambda}}{\frac{v}{\lambda}}$

$\nu'=2\nu$

The new frequency of sound wave is twice the initial frequency.

Percentage of change in frequency=$\frac{2\nu-\nu}{\nu}\times 100=\frac{\nu}{\nu}\times 100=100$%

Hence, the percentage  change in its frequency will be =100%

#Learns more:

https://brainly.in/question/7116468:answered by Fatimaroohee

Answer 2

Answer:

100%

Explanation: