Speed of Sound Wave question

[betterfuture]

So from my understanding, the speed of a particle in a medium is fixed and only changes if the medium changes. That means velocity is not dependent on the frequency or wavelength. So if frequency get bigger, wavelength has to get smaller to the same degree because, again, the speed does not change in a medium.

However, is it true that as one goes from say air to water the speed changes and travels faster, and only the wavelength will change AND NOT the frequency? And why is this so?

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[aldol16]

However, is it true that as one goes from say air to water the speed changes and travels faster, and only the wavelength will change AND NOT the frequency? And why is this so?

This is essentially a conservation of energy problem. Imagine being an outside observer looking at the interface between air and water. You can "see" the sounds waves coming from the water and then exiting into the air. Imagine a sound wave moving at a frequency of 100 Hz, or 100 waves/s. This means that at any given point in the water, 100 waves will pass through in a second. Okay, now you make a transition into the air. What would happen if frequency could change? Well, since the speed of sound is slower in air as compared to water, we can say that frequency drops to 50 Hz. Here, for simplicity, we will assume that wavelength (the only other determinant of wave speed) does not change. Therefore, at the point just before the wave exits the water, you will see 100 waves move past that point in a second. Then, at the point just after the wave exits the water, you will see 50 waves move past that point in a second.

Where did the other 50 waves go? They can't just spontaneously disappear. Well, then they would have had to pile up at the interface of the air and water. Every second, 50 more waves get "trapped" at that interface because they can't exit - air can only sustain the 50 waves/s and there are 100 waves/s trying to get out of the water. This would become unsustainable very quickly.

This doesn't actually happen - it was just a thought experiment. So if we observe that frequency cannot change because waves can't build up on one side of an interface because of conservation of energy, we can only conclude that wavelength changes.

 

[betterfuture]

Then what about for speed of light? Speed of light does not require a medium so I am guessing speed is always 3*10^8m/s, correct? Both frequency and wavelength here do change.

 

[aldol16]

Then what about for speed of light? Speed of light does not require a medium so I am guessing speed is always 3*10^8m/s, correct? Both frequency and wavelength here do change.

Apparent speed of light does depend on what it's traveling in. That's the basis of index of refraction. Not only that, but when light refracts, frequency also does not change - only wavelength.

 

[betterfuture]

Alright, thanks

 

[Astra]

This is essentially a conservation of energy problem. Imagine being an outside observer looking at the interface between air and water. You can "see" the sounds waves coming from the water and then exiting into the air. Imagine a sound wave moving at a frequency of 100 Hz, or 100 waves/s. This means that at any given point in the water, 100 waves will pass through in a second. Okay, now you make a transition into the air. What would happen if frequency could change? Well, since the speed of sound is slower in air as compared to water, we can say that frequency drops to 50 Hz. Here, for simplicity, we will assume that wavelength (the only other determinant of wave speed) does not change. Therefore, at the point just before the wave exits the water, you will see 100 waves move past that point in a second. Then, at the point just after the wave exits the water, you will see 50 waves move past that point in a second.

Where did the other 50 waves go? They can't just spontaneously disappear. Well, then they would have had to pile up at the interface of the air and water. Every second, 50 more waves get "trapped" at that interface because they can't exit - air can only sustain the 50 waves/s and there are 100 waves/s trying to get out of the water. This would become unsustainable very quickly.

This doesn't actually happen - it was just a thought experiment. So if we observe that frequency cannot change because waves can't build up on one side of an interface because of conservation of energy, we can only conclude that wavelength changes.

Your way of teaching and explaining material is beautiful.

Thank you so much! I was gonna post this question but you already explained it!

So when a prism splits light into its different colors, It is due the fact that the light has been split into different wavelengths? This difference in wavelengths is what gives us the rainbow of colors?

Also, I was reading up on refraction.

I learned that the speed of light does not change but the velocity does only do to the fact that the light "bounces" around more in the media, causing a slower velocity.

Correct?

 

[aldol16]

Your way of teaching and explaining material is beautiful.

Thank you so much! I was gonna post this question but you already explained it!

So when a prism splits light into its different colors, It is due the fact that the light has been split into different wavelengths? This difference in wavelengths is what gives us the rainbow of colors?

Also, I was reading up on refraction.

I learned that the speed of light does not change but the velocity does only do to the fact that the light "bounces" around more in the media, causing a slower velocity.

Correct?

Thank you! I try to explain it in intuitive terms so people can grasp the underlying principles, which has been demonstrated to be better for learning and retaining the material.

Yes, when light enters a prism, it refracts and slows down and so the prism "splits" the light into its constituent wavelengths. You can think about it like this. White light is composed of all the wavelengths of light. Light of different wavelengths slows down to different extents when it enters the prism. This is because of E = hf = hc/lambda. The energy of the light is constant - that's conservation of energy. I just told you that the frequency is also constant because of the explanation above. And so for E = hc/lambda to remain constant, the speed of light - c - in the prism must change according to the wavelength. That is, the speed will change more for a higher wavelength than for a lower wavelength. That gives you the specific ordering of wavelengths of light coming out of the prism. Note, however, that I'm referring here to only the apparent speed of light, because the speed of light is constant in all frames of reference.

That brings me to my second point. The speed of light is constant in all reference frames. The reason the apparent speed of light is different in air versus water, for example, is because water is more dense and thus the light will "bounce off" the particles in water and take a non-linear path to the other side, although the sum of all light particles will have an overall directionality. Therefore, you would expect the apparent velocity of light to be lower in water than in air. Lower velocity = higher refractive index and this, of course, is what you observe. This, of course, relies on the particle nature of light.

 

[Astra]

Thank you! I try to explain it in intuitive terms so people can grasp the underlying principles, which has been demonstrated to be better for learning and retaining the material.

Yes, when light enters a prism, it refracts and slows down and so the prism "splits" the light into its constituent wavelengths. You can think about it like this. White light is composed of all the wavelengths of light. Light of different wavelengths slows down to different extents when it enters the prism. This is because of E = hf = hc/lambda. The energy of the light is constant - that's conservation of energy. I just told you that the frequency is also constant because of the explanation above. And so for E = hc/lambda to remain constant, the speed of light - c - in the prism must change according to the wavelength. That is, the speed will change more for a higher wavelength than for a lower wavelength. That gives you the specific ordering of wavelengths of light coming out of the prism. Note, however, that I'm referring here to only the apparent speed of light, because the speed of light is constant in all frames of reference.

That brings me to my second point. The speed of light is constant in all reference frames. The reason the apparent speed of light is different in air versus water, for example, is because water is more dense and thus the light will "bounce off" the particles in water and take a non-linear path to the other side, although the sum of all light particles will have an overall directionality. Therefore, you would expect the apparent velocity of light to be lower in water than in air. Lower velocity = higher refractive index and this, of course, is what you observe. This, of course, relies on the particle nature of light.

Thank you so much for the detailed response!

I am very grateful for your presence in the forums. If it wasn't for you, I would be spending hours simply searching for answers before I could even comprehend them!

 

[aldol16]

I'm sure you could easily find the answers elsewhere! I find teaching others these concepts to be really good for remembering them and understanding them myself. Some questions are actually quite detailed and thought-provoking!