Wave Exercises

Propagation Speed

1. The graph below represents a wave that propagates at a speed of 300m / s.


a) the amplitude of the wave;

The amplitude of the wave is given by the distance from the origin to the crest of the wave, ie:

b) the wavelength;

The wavelength is given by the distance between two ridges or between 3 nodes, ie:

As the figure shows the measurement of three "half wavelengths", we can calculate it:

c) the frequency;

Knowing the propagation speed and wavelength, we can calculate the frequency through the equation:

Substituting the values ​​in the equation:

d) the period.

Since the period is equal to the inverse of frequency:

Wave refraction

1. A vibrating needle produces waves with a propagation velocity of 160m / s and a wavelength of 1mm, arriving at a depth difference of 45 ° and being refracted. After changing depths the refracted angle becomes 30 °. What is the new wave progression speed?

And the length of the refracted waves?

Using Snell's Law:

Using the relation with propagation velocities, we arrive at the equation:

The speed of the refracted wave will be 113.1m / s.

To calculate the refracted wavelength, we use Snell's Law, using the relationship with wavelengths:

The refracted wavelength will be 0.7mm.

Note that the result appears in millimeters because units were not converted to SI at the beginning of the resolution.