Question

If the distance between 1st crest and the third crest is 8 m. What is the wavelength of a transverse wave?
(A) 4 m
(B) 8 m
(C) 5 m
(D) 6 m

Answer 1

Hint: The wavelength ($\lambda $) is the distance between two successive crests in a transverse wave. Wavelength can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave.

Complete step by step solution:
A wave is a disturbance that propagates, or moves from the place it was created. The simplest waves repeat themselves for several cycles and are associated with simple harmonic motion.
A simple wave consists of a periodic disturbance that propagates from one place to another. The wave propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation.
The distance between 1st and 2nd crest is $\lambda $. And the distance between each successive crest is the same in the transverse wave.
Thus, the distance between 1st crest and 3rd crest is given
$
2\lambda = 8m \\
\lambda = 4m \\
$
Hence the wavelength of the given transverse wave is 4 m.

Wavelength of the wave = Speed of the wave/ Frequency.

Note: Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave). Crest is the highest point of the wave whereas the trough is the lowest. Since wavelength is distance/length, it is measured in units of lengths such as metres, centimetres, millimeters, nanometres, etc. Wavelength is inversely proportional to frequency. This means the longer the wavelength, the lower the frequency. In the same manner, shorter the wavelength, higher will be the frequency.