A wave created by a certain source travels from medium 1 into another medium 2.

Question

A wave created by a certain source travels from medium 1 into another medium 2. It is noticed that its velocity is faster in medium 2 than in medium 1. Three students are discussing what happens to the properties of the wave as it moves into medium 2. Student 1: The frequency of this wave increases as this waves moves into medium 2 in order to keep the equation of the velocity of a wave valid. Student 2: No, the frequency of the wave will remain the same as it is only dependent on the source, it will be the wavelength that will increase in order to keep the equation of the velocity of a wave valid. Student 3: No, you are both wrong. Both parameters will adjust in order to keep the equation of the velocity of a wave valid. Which of these students, if any, do you agree with? Justify your response with words and/or equations.

Explanation / Answer

The equation of velocity of wave is given by :

v= f

Where is the wavelength of the wave and f is the frequency of the wave.

As velocity of wave is more in medium 2 only the wavelength of the wave will increase in order to keep the equation of the velocity of wave valid and frequency will not change at all..

Reasons :

Continuity of the wave motion can answer why frequency of wave does not change. Imagine you had a change in frequency going from medium 1 to medium 2- say 50 Hz become 100 Hz.

How do you make something move at 100 Hz? You need to apply a driving force at 100 Hz of course. But the incoming wave is going at 50 Hz.

To add energy to the wave we must be pushing when it it moving away from us and pulling when it is moving towards us. If you move too slowly to keep up you can't give the faster moving wave any energy.

The only way to be in sync is to have the same frequency.

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