Question

What is the wavelength if the distance between a crest and an immediate trough in a transverse wave is $15m$?
$\begin{align}
  & A.30m \\
 & B.40m \\
 & C.50m \\
 & D.15m \\
\end{align}$

Answer 1

Hint: First of all draw a diagram of a transverse wave and mark the crest and the trough. The distance between these will be equal to half of the wavelength of the wave. Substitute the values in this equation and find the answer.

Complete step by step answer:
Wavelength is the distance between the identical points, that is, consecutive crests in the consecutive cycles of a waveform signal which is propagated in space or along a wire. The length is taken in meters usually. In short, we can say that the wavelength is given as the distance between adjacent crest and crest or trough and trough.
Here in this question, it is mentioned that the distance has been measured between a crest and adjacent trough.

Hence we can say that the distance between the consecutive crest and trough will be equal to half of the wavelength of the wave.
Therefore we can write that,
$15=\dfrac{\lambda }{2}$
Where $\lambda $ the wavelength given in meters is.
Rearranging this equation will give,
$\lambda =30m$
Therefore the correct answer is option A.

Note: In a transverse wave, the particles of the medium are in motion perpendicular to the direction of the wave to travel. Transverse waves have properties by peaks and valleys, known as crests and troughs. In a longitudinal wave, the particles of the medium are in motion parallel to the direction of the wave of travel. Light is a transverse wave since its components are in vibration perpendicular to the direction of propagation. This is a major example of a transverse wave. And also sound is an example of longitudinal waves.