Question

A sine wave is travelling in a medium. What is the minimum distance between two particles always having the same velocity is
A.\[\dfrac{\lambda }{2}\]
B.\[\dfrac{\lambda }{4}\]
C.\[\dfrac{{3\lambda }}{2}\]
D.\[3\lambda \]

Answer 1

Hint: The sine or sinusoidal wave is a curve that is defined by trigonometric function y=sin x. It is used to generate any other waveform of any type. The curve of the sine wave moves smoothly above and below the zero point on the graph forming a perfect S-shape.

Complete step by step solution:
The sinusoidal or sine wave has both maximum and minimum points. This distance can be known if the wavelength is known. The wavelength of the wave is the distance travelled by the particle from its mean position to complete one vibration. One vibration is completed when the particle travels a distance equal to one crest and one trough. The distance between two successive crests or troughs can be used to find the distance.

Also it is given that the particles are always having the same velocity. If suppose \[\lambda \] is the wavelength of the sine wave and if two of the particles are moving in a medium, then the minimum distance will be \[\dfrac{\lambda }{2}\] as the velocity is same but direction is opposite. Therefore, the minimum distance between two particles always having the same velocity is \[\dfrac{\lambda }{2}\].

Hence, Option A is the correct answer.

Note: A wave is produced when the particles of a medium transfer disturbance from one particle to next without actually moving themselves. This type of motion basically carries energy. Though all the sine waves appear to be similar, they are not. Considering factors like amplitude and frequency, one sine wave can be differentiated from another.