Question

In a ripple tank, 15 full ripples are produced in one second, if the distance between the trough and the next crest is 20c. Calculate the velocity of the wave.
A) \[200\dfrac{{cm}}{s}\]
B) \[400\dfrac{{cm}}{s}\]
C) \[600\dfrac{{cm}}{s}\]
D) \[800\dfrac{{cm}}{s}\]

Answer 1

Hint-The highest positive point in a wave is called a ‘crest’ and the highest negative point in a wave is called ‘trough’. And the distance between the two maximum peaks of a wave is called wavelength. And the total number waves in a certain time period is called frequency. We can also say that the reciprocal of time is called frequency.

Formula used:
\[V = \lambda f\]
Where,
\[V\]= velocity
\[\lambda \]= wavelength
\[f\]= frequency

Complete step by step answer:
(i) In the ripple tank, 15 full ripples are produced in one second. There are fifteen oscillations in the time of one second.
\[\therefore f = \dfrac{{15}}{1}\]
\[ \rightarrow f = 15Hz\]
(ii) The distance between two crests is called wavelength\[(\lambda )\]. And the centre of the wavelength and the trough is half of the wavelength\[\left( {\dfrac{\lambda }{2}} \right)\]. Therefore the distance between the crest and the next trough is \[\dfrac{\lambda }{2}\]which equals to \[20cm\]
\[\dfrac{\lambda }{2} = 20\]
\[ \rightarrow \lambda = 40cm\]
(iii) The velocity of the ripples wave is, \[V = \lambda f\]
\[ \rightarrow V = 40 \times 15\]
\[\therefore V = 600\dfrac{{cm}}{s}\]

Hence the correct option is C.

Additional information:
The Ripple tank is a shallow glass full of water. This ripple tank is used to showcase the properties of waves. The formed ripples are similar to the waves. This wave's crest and the trough. The crest represents the bright spots as it absorbs more light and the trough represents the dark spots.

Note: In the ripple tank, the ripples are produced on the illumination of light. This causes the ripples in the water. These ripples show as a wave having crest and the trough which demonstrate the principles like reflection, refraction and the diffraction of the waves. This wave has its own velocity, frequency and the wavelength.