(I) Electromagnetic waves and sound waves can have the same fr...

Question

(I) Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of a 1.00-kHz electromagnetic wave? (b) What is the wavelength of a 1.00-kHz sound wave? (The speed of sound in air is 341 m/s.) (c) Can you hear a 1.00-kHz electromagnetic wave?

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A laser pointer emits light at a frequency of 4.74 multiplied by 10 to the power of 14 Hertz A. What is the wavelength of this light? B? What would be the wavelength if a sound wave had a frequency of 4.74 multiplied by 10 to the power of 14 Hertz and could propagate through a diamond with a speed of 12,000 m per second. C. Is it possible for human eyes to detect sound waves? Awesome. So it appears for this particular problem we're asked to solve for three separate answers. For part A, we're trying to figure out what the wavelength of light is. B we're trying to figure out what the wavelength would be for a sound wave that had a frequency of 4.74 multiplied by 10 to the power of 14 Hertz. And that could propagate through a diamond with a speed of 12,000 m per second and then our third answer that we're trying to solve for us, we're trying to figure out whether or not human eyes are able to detect sound waves. Awesome. So now that we know that we're solving for three separate answers, let's read off our multiple choice answers to see what our final answer set might be noting that for parts A and B, they're all in the same units of meters. Awesome. So A is for part A 6.3 multiplied by 10 to the power of negative seven, B is 2.5 multiplied by 10 to the power of negative 11. And C is no, B part A is 3.3 multiplied by 10 to the power negative seven and 2.2 sorry 2.5 multiplied by 10 to the power negative 11. And C is yes. And then C for A is 3.3 multiplied by 10 to the power of negative seven and B is 2.9 multiplied by 10 to the power of negative 11. And C is no. And finally, for D for part A is 6.3 multiplied by 10 to the power in negative seven and B is 2.9 multiplied by 10 to the power negative 11 and C is yes. OK. So first off, we need to recall and use the equation that helps us solve for the wavelength of light. And in order to do that, we need to recall and use the relationship between the speed of light frequency and wavelength. So as we should recall, we should say that C the speed of light within a vacuum is equal to the wavelength multiplied by the frequency. And let's quickly make a note here in case we can't remember off the top of our head that C the speed of light in a vacuum is equal to 3.0 multiplied by 10 to the power of eight. And its units of measurement are meters per second. Awesome. And once again, lambda represents the wavelength and F is the frequency and of course, C is the speed of light. OK. Moving right along here. So now we need to rearrange this equation to isolate and solve for a Lambda means we're trying to solve for the wavelength of light. So when we use a little bit of Algeri to get Lambda by itself, you will find that Lambda is equal to the speed of light divided by the frequency. So now all we need to do is plug in our known variables to solve for lambda. So we know that the speed of light is 3.0 multiplied by the multiply by 10 to the power of 8 m per second is that our speed of light divided by our frequency, which our frequency is given to us as 4.74 multiplied by 10 to the power of 14 Hertz. So when we plug that into our calculator and we round to two decimal places. We will find that our wavelength is approximately equal to 6.33 multiplied by 10 to the power of negative 7 m. Fantastic, which we can easily just round it just to one decimal place. So we could just say 6.3 multiplied by 10 to the power negative 7 m. Because as we can see all of our multiple choice answers are rounded to one decimal place. Awesome. And that is our first answer. Hooray, we did it. So now we need to solve for part B. So just in case we get confused, we'll just make a little A here. And now we're solving for part B. So for part B, we're trying to figure out the wavelength of a sound wave within a diamond. So we're gonna be using this a similar formula to help us solve for the sound wave. So let's say that in this case, we're dealing with V is equal to lambda multiplied by frequency. So the wavelength lambda multiplied by F the frequency and V in this case, V is different because instead of using the speed of light, we're using V and V in this case is equal to 12,000 m per second because this is how long it takes the, so this is the how a sound wave or a wavelength of sound will propagate through a diamond with a speed of 12,000 m per second. Awesome. So with that in mind, so now we need to rearrange this equation to isolate and solve for Lambda. So we'll find that Lambda is equal to V divided by F Awesome. So the wavelength is equal to V divided by the frequency. Awesome. So now we just need to plug in our known variable. So we know that V is equal to 12,000 m per second. We need to divide it by our frequency which our frequency is still the same. It's 4.74 multiplied by 10 to the power of 14 Hertz. So let me plug that into our calculator. We will find that it's approximately equal to when we round to one decimal place, 2.5 multiplied by 10 to the power of negative 11 m. And that is our final answer for part B per we did it. So I'll make a little note here for A and for B now we could start solving for part C and part C can human eyes detect sound waves? The answer is no. And we know that the answer is no because we, as we should recall and note human eyes cannot detect sound waves. Human eyes are sensitive to electromagnetic waves specifically within the visible light spectrum and not mechanical waves such as sound sound waves require a medium to propagate and are detected by the human ear, not by the eyes. That's why the answer is no. So looking at our multiple choice answers. The correct answer set has to be for multiple choice answer a letter A which states that A is 6.3 multiplied by 10 to the power of negative 7 m. B is 2.5 multiplied by 10 to the power of negative 11 m and C is no. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

(I) Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of a 1.00-kHz electromagnetic wave? (b) What is the wavelength of a 1.00-kHz sound wave? (The speed of sound in air is 341 m/s.) (c) Can you hear a 1.00-kHz electromagnetic wave?

Key Concepts

Wavelength

Wave Speed

Nature of Electromagnetic Waves vs. Sound Waves

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