Question

A sinusoidal wave is propagating along a stretched string that lies along the x-axis. The displacement of the string as a function of time is graphed in Fig. E15.11 for particles at \({\bf{x}}{\rm{ }} = {\rm{ }}{\bf{0}}\) and at\(x = 0.0900 m\). (a) What is the amplitude of the wave? (b) What is the period of the wave? (c) You are told that the two points \({\bf{x}}{\rm{ }} = {\rm{ }}{\bf{0}}\) and \(x = 0.0900 m\) are within one wavelength of each other. If the wave is moving in the +x direction, determine the wavelength and the wave speed. (d) If instead the wave is moving in the –x direction, determine the wavelength and the wave speed. (e) Would it be possible to determine definitively the wavelengths in parts (c) and (d) if you were not told that the two points were within one wavelength of each other? Why or why not?

Short answer

(a) The maximum \(y\) or amplitude is\(4\,mm\).

Step-by-step solution

Given data

Fig. E15.11

Location of particles at \(x = 0\)and \(x = 0.0900 m\)

Concept/ Formula used

Amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave may move relative to its equilibrium location. It is equivalent to the vibration path's half-length.

Calculation for Amplitude

(a)

From graph it is clear that the maximum displacement of wave relative to equilibrium distance is\(4\,mm\).

i.e. The maximum \(y\) or amplitude is \(4\,mm\).