Question

Marbles are being dropped into the surface of water to create ripple.It it's given that the velocity of the wave in water is V and the moment a marble drops into the surface, another marble is dropped from height h, What will the wavelength of the waves be generated?

Answer 1

Step:1 Given Data

The velocity of the wave, v = V m/s

Height from which marble is dropped is = h

Acceleration due to gravity = g

We need to find the wavelength of the waves generated.

Step:2 Formula used

The time period of the wave generated = the time taken between two marbles to drop (T) $=2\times \left(\sqrt{\frac{2h}{g}}\right)$

$Frequency\left(f\right)=\frac{1}{Time\left(T\right)}$

Step:3 Calculation of wavelength

$\Rightarrow Frequency,f=\frac{1}{2\sqrt{{\displaystyle \frac{2h}{g}}}}$

$Wavelength\left(\lambda \right)=\frac{Velocity\left(v\right)}{Frequency\left(f\right)}$

By putting the value, we get

$Wavelength\left(\lambda \right)=\frac{V}{{\displaystyle \frac{1}{2\sqrt{{\displaystyle \frac{2h}{g}}}}}}=\left(2V\sqrt{\frac{2h}{g}}\right)$

Hence, the wavelength of the waves generated is, $Wavelength\left(\lambda \right)=\frac{V}{{\displaystyle \frac{1}{2\sqrt{{\displaystyle \frac{2h}{g}}}}}}=\left(2V\sqrt{\frac{2h}{g}}\right)$.