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A series of ocean waves, each \[5.0{\text{ }}m\] from crest to crest, moving past the observer at a rate of 2 waves per second. What is the velocity of the ocean waves?
A. \[2.5{\text{ }}m/s\]
B. \[5.0{\text{ }}m/s\]
C. \[8.0{\text{ }}m/s\]
D. \[10.0{\text{ }}m/s\]

Last updated date: 24th Jul 2024
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Hint: The velocity at which a wave propagates is given by the equation $v = \nu \lambda $, \[\nu \]is the frequency and $\lambda $ is the wavelength of the wave.

Complete step by step answer:The distance between two consecutive crests is known as the wavelength of the wave. It is given that the wavelength of the ocean wave is \[5{\text{ }}m\] . That is, $\lambda = 5$
Frequency of the waves is 2 waves per second, that is $\nu = 2$
Wave velocity of the waves is given by $v = \nu \lambda = 5 \times 2 = 10\,m/s$
Hence, the correct option is (D).

Note:There are two types of waves, longitudinal and transverse. Ocean waves are transverse in nature. In transverse waves, a crest is the portion of the medium, which is raised temporarily above the normal position of the rest of the particles of the medium. Wavelength of a wave is the length of one wave. It is equal to the distance travelled by the wave during the given time; any one particle of the medium completes one vibration about its mean position. Frequency of the vibration of the particle is defined as the number of vibrations completed by the particle in one second. The wave velocity v is determined only by the elastic and the inertial properties of the medium, therefore v is constant for a given medium. Frequency \[\nu \] is characterized by the source which produces disturbance. Different sources may produce vibrations of different frequencies. Their wavelengths will differ to keep the product $v = \nu \lambda $ constant.