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(II) Two automobiles are equipped with the same s…

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Problem 63 Hard Difficulty

(II) (a) Compare the shift in frequency if a 2300 -Hz source is moving toward you at 18 $\mathrm{m} / \mathrm{s}$ , versus you moving toward it at 18 $\mathrm{m} / \mathrm{s}$ . Are the two frequencies exactly the same? Are they close? (b) Repeat the calculation for 160 $\mathrm{m} / \mathrm{s}$ and then asymmetry of the Doppler formulas? (d) Show that at low speeds (relative to the speed of sound), the two formulas- source approaching and detector approaching-yield the same result.

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 16

Sound

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Video Transcript

but a for 18 meter per second related velocity. 15 meter per second over relative velocity. Our F dish off source moving. So I will write s o our source and M for moving. Uh, that is equal toe frequency over one minus were lost. You over Source. So so are Or, um the speed off the sound. We have frequency here. That is a 23 100 2300 or ah, let you lost. Here is 18. So our sources 18 here, um, divided by the speed of the sound, which is 3 43 Um, dividing these two numbers. The answer we get here approximately four Source movie. Is this 20 4 30? Hers 24. 30 hertz, Um, for frequency for observer moving. So we'll be observer movie. So I read em for Movie is given by the formula Frequency times one plus there. Ah, speed of the source Over the speed of sound. Yes, Uh, by plugging the values as we did above then the answer here we get here is a 24 uh, 20 hearts. Before going to yours, we can complete the spreading frequencies by using the formula. Oh, jeez. If source uh, for our source s or sore, huh? Also moving. Object. Um, minus their frequency over the source offer an observer moving divided by the frequency over us source. And if we divide those terms, then the spread in frequencies we get here is a 0.26% in part B were asked to do the same thing, but for the religion velocity, which is, um, which is 1 60 meter per second, we have to do the same thing, but for a different velocity. So we will use the same formula. Um, so FDA source, which is moving m. That will be 43 10 arse. So if I plug the value of 1 60 meter for a second, the velocity of a source in the equation, then answer Here I get is a 4310 hertz. Similarly, for the frequency for observer moving, which is obeah. So being them if I plugged the value off 1 60 this formula, then Ah, the value here I get is three, 3 70 hurts 70 bars. Similarly, as I did in there, but a if I want to complete the shift in ah frequencies, then The shift I get here is shift I get here is it's all right, Asai shift shift I get here is equal to 41%. So the shift I have here, he's 41% for the relative velocity off 1 60 meters per second. Let me open another page for part C. When we have a relative velocity over 3 20 3 20 meter per second, then I have their frequency off a source movie source Moving I get here is a 34 1003 100 hers. So sorry. It looks like aids. So this is three our 300 herds, 34,300 hers similarly using the same formula. Then I get to the frequency off the observer movie. Uh, and for a movie I get here is approximately 4000 450 hearts by using the same method is I didn't part, eh? I can complete the spread in frequencies, and the shift I get here is he's 1300%. This is 3 1300%. Um, but D, if we assume, are the velocity or the speed off the source to be much less than they're speed off the sound, then my frequency off. A source. Moving source moving. I can. Right here. You f one minus. We off the source. Over us. Speed off the sound. So this is me? Yes, or minus one minus one. And if I do the bio mia expansion for the assumption I made above then, uh, the question I get here is f into one plus Ah, speed off the source source over the speed off their sound. And this is equal to a CZ we saw earlier. This is equal to, um, the frequency off the observer movie observer movie. Hence, we proved here that for very small velocities off the source has compared the speed off their sound that the frequencies off a source moving is equal to the frequency. Um, off the observer movie. End off the problem. Thank you for watching

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Physics for Scientists and Engineers with Modern Physics

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(II) Two automobiles are equipped with the same s…

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Physics for Scientists and Engineers with Modern Physics

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Watch More Solved Questions in Chapter 16

Video Transcript

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Farnaz Mohseni

Jared Enns

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Farnaz Mohseni

Jared Enns

Meghan Miholics

Douglas C. GiancoliPhysics for Scientists and Engineers with Modern Physics

Elyse Gonzalez

Farnaz Mohseni

Jared Enns

Meghan Miholics

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics