Question

In a ripple tank, 10 full ripples/s are produced. The distance between peaks of consecutive trough and crest is \[15\,{\text{cm}}\]. Calculate the velocity of ripples.
A. \[2\,{\text{m/s}}\]
B. \[3\,{\text{m/s}}\]
C. \[4\,{\text{m/s}}\]
D. \[6\,{\text{m/s}}\]

Answer 1

Hint:Use the formula for velocity of the wave. This formula gives the relation between velocity of the wave, frequency of the wave and wavelength of the wave. From the given information, determine the frequency of the ripples. Then recall the concept of wavelength of the wave and determine wavelength of the wave. Substitute all values in the formula and calculate velocity of the wave.

Formula used:
The formula for velocity \[v\] of a wave is given by
\[v = n\lambda \] …… (1)
Here, \[n\] is frequency of the wave and \[\lambda \] is wavelength of the wave.

Complete step by step answer:
We have given that in a ripple tank, 10 ripples are produced in one seconds. The ripple produced in the water is also a type of wave. Hence, the frequency of the ripples in the ripple tank is \[10\,{\text{Hz}}\] i.e, \[n = 10\,{\text{Hz}}\].We have also given that the distance between the peaks of the consecutive trough and crest is \[15\,{\text{cm}}\].The wavelength of a wave is the distance between two consecutive crests or troughs in the wave.Hence, the distance between consecutive trough and crest is half of the wavelength of the wave. Hence, we can write
\[\dfrac{\lambda }{2} = 15\,{\text{cm}}\]
\[ \Rightarrow \lambda = 2\left( {15\,{\text{cm}}} \right)\]
\[ \Rightarrow \lambda = 30\,{\text{cm}}\]
Hence, the velocity of the wave is \[30\,{\text{cm}}\].

Convert the unit of wavelength of the wave in the SI system of units.
\[\lambda = \left( {30\,{\text{cm}}} \right)\left( {\dfrac{{{{10}^{ - 2}}\,{\text{m}}}}{{1\,{\text{cm}}}}} \right)\]
\[ \Rightarrow \lambda = 0.30\,{\text{m}}\]
Let us now calculate the velocity of the ripple wave.Substitute \[10\,{\text{Hz}}\] for \[n\] and \[0.30\,{\text{m}}\] for \[\lambda \] in equation (1).
\[v = \left( {10\,{\text{Hz}}} \right)\left( {0.30\,{\text{m}}} \right)\]
\[ \therefore v = 3\,{\text{m/s}}\]
Therefore, the velocity of the ripples is \[3\,{\text{m/s}}\].

Hence, the correct option is B.

Note:The students may think that how can we use the formula for velocity of a wave to solve this question. But the students should keep in mind that ripples on water are also a type of wave i.e. transverse wave. Also it should be kept in mind that the value 10 ripples per second given in the question is the frequency of the ripples.