What happens to wavelength and frequency when a wave changes velocity

[HorseBox]

When an EM wave goes into say a denser medium and its velocity is decreased how does its wavelength and frequency change? I read that the frequency remains constant but the wavelength changes. Is this true? If so does that mean the wave gets compressed when it enters a denser medium. Does the amplitude decrease too?

 

[jfy4]

The index of refraction specifically states the change in wave-length for a em-wave.

$$n=\frac{\lambda}{\lambda_{n}}$$

and the relation for velocity-a medium- and light is

$$n=\frac{c}{v}$$

that gives a simple answer to your question. does it help?

 

[Simon43254]

Or if you wish to think of it "graphically" then imagine a wave heading into an object, say glass at a specific angle. What happens to the first part of the wave that hits the glass?... you can think of it like the first part of the wave gets slowed down, before the other part catches up. Now draw this, and you'll notice that the waves tend to get bunch up. Now make deductions based on the fact that you know the velocity has decreased.

 

[HorseBox]

Ah yeah that explains it thanks. I do like to understand things visually first then use the mathematical approach to verify my understanding and unravel things I wouldn't have spotted.

 

[PJC01]

I can confirm that when a wave enters a denser medium and its velocity decreases, the wavelength does indeed change while the frequency remains constant. This is known as the principle of wavelength and frequency invariance, which states that the product of wavelength and frequency of a wave remains constant as it travels through different mediums.

To understand this phenomenon, we must first understand the relationship between wavelength, frequency, and velocity. Wavelength is the distance between two consecutive peaks or troughs of a wave, while frequency is the number of complete cycles of the wave that pass a given point in one second. Velocity, on the other hand, is the speed at which the wave travels.

According to the equation v = λf, where v is velocity, λ is wavelength, and f is frequency, we can see that if the velocity decreases, the wavelength must also decrease in order for the frequency to remain constant.

This change in wavelength can be visualized as the wave getting compressed when it enters a denser medium. This is because in a denser medium, the particles are closer together, and the wave must travel a shorter distance between each particle, resulting in a shorter wavelength.

However, the amplitude of the wave does not necessarily decrease when it enters a denser medium. The amplitude of a wave is the height of the peaks or depth of the troughs, and it is determined by the energy of the wave. While the velocity and wavelength may change, the energy of the wave remains constant, so the amplitude may stay the same or even increase in some cases.

In summary, when a wave enters a denser medium and its velocity decreases, the wavelength changes while the frequency remains constant. This is due to the principle of wavelength and frequency invariance. The wave may appear compressed, but the amplitude may not necessarily decrease.