Question

The sinusoidal wave shown in the figure below is traveling in the positive x-direction and has a frequency of 53.7 Hz.

A sinusoidal wave is plotted on a coordinate plane. The wave is vertically centered on the horizontal axis. The vertical distance between a crest and a trough is 8.26 cm, and the horizontal distance between a crest and the nearest trough is 4.20 cm.

(a) Find the amplitude.
cm

(b) Find the wavelength.
cm

Answer 1

Amplitude of the wave is defined as the peak value either of a crest or a trough i.e The maximum value from the horizontal axis to vertically maximum distance. Here we are given that the distance between crest( vertically maximum point) and the trough(maximum value in downward direction) is 8.26cm so amplitude will be simple the distance between horizontal axis to vertically maximum distance or we call it crest. Hence amplitude =8.26cm/2=4.13cm.

B) Similarly the distance between two successive crest and trough gives us wavelength and the distance between a crest and a trough gives us the value half value of the wavelength. So wavelength = 2*distance between crest and a trough. We get 2*4.2=8.40cm.

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