Explanation:

When a stone is thrown in a pond, it disturbs the surface of water and produces ripples. These ripples are a form of wave that travel through the water. The properties of these waves can be described in terms of their wavelength and velocity.

Wavelength:

The wavelength of a wave is the distance between two consecutive crests or troughs of the wave. In this case, we are given that the distance between a crest and trough is 10 centimeters. Since there are 12 full ripples produced in one second, the wavelength can be calculated as follows:

Wavelength = Distance traveled by wave in one second / Number of full ripples produced in one second

The distance traveled by the wave in one second is equal to the velocity of the wave. Therefore, we can rewrite the above equation as:

Wavelength = Velocity / Number of full ripples produced in one second

Substituting the given values, we get:

Wavelength = Velocity / 12

Velocity:

The velocity of a wave is the speed at which the wave travels through the medium. In this case, the medium is water. The velocity of a wave can be calculated using the following formula:

Velocity = Wavelength x Frequency

Here, the frequency of the wave is the number of full ripples produced in one second, which is 12.

Substituting the given values, we get:

Velocity = 10 cm x 12 = 120 cm/s

Therefore, the wavelength of the wave is equal to the velocity of the wave divided by the number of full ripples produced in one second, which is:

Wavelength = 120 cm/s / 12 = 10 cm

And the velocity of the wave is equal to the wavelength of the wave multiplied by the frequency of the wave, which is:

Velocity = 10 cm x 12 = 120 cm/s

Hence, the wavelength and velocity of the wave can be calculated using the given information.

Wave length = 10×2=20(20/100m)
velocity=frequency/wave length
=12×20/100= 240/100m/s
velocity=2.4m/s