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Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470 Hz as the truck rece...

Question

Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470 Hz as the truck recedes, you hear a tone of 420 Hz

Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470 Hz as the truck recedes, you hear a tone of 420 Hz



Answers

Hearing the siren of an approaching fire truck, you pull over to
the side of the road and stop. As the truck approaches, you hear
a tone of $460 \mathrm{Hz} ;$ as the truck recedes, you hear a tone of 410 $\mathrm{Hz}$ .
How much time will it take for the truck to get from your position to the fire 5.0 $\mathrm{km}$ away, assuming it maintains a constant speed?

In this exercise, we have a fire truck that when at rest emits sound signal at a frequency off 1400 hertz. And we have someone standing on the side of the road that sees the fire truck coming towards her and years of frequency of 1600 hertz. And our goal is to find what is the speed off the fire trip? Yeah, well, this is Ah, Doppler effect problem. So let me briefly review the Doppler effect before we solve this exercise. So, basically, the doctor of the perfect concerns the change in frequency by moving objects, both objects that move while admitting sound and objects that move while receiving. So so have that the frequency received by an observer is equal to the speed of sound, see, plus or minus the speed off the receiver. That is the speed of the observer divided by C plus or minus the speed off the source times F 00 is the frequency that is emitted by the, uh, by the source. In our case, a zero is 1400 hertz. Uh, notice that the blood sign here is used in the numerator is used when the receiver is moving towards the source. The minus sign is used when the receiver is moving away from the source and the denominator the plus sign is used when the source is moving away from the receiver and the minus sign when the source is moving towards there, is here. In our case, we have the receiver that is the person who is standing on, uh, the side of the road. Since she stayed standing, she's still relative to the air, so her speed is zero. And the speed of the source that is the speed of the fire truck is the speed TV that we want to fight. And we have the information that the fire truck is moving towards her. So this means that we must use the minus. Okay, so we have every information we need in order to calculate V. So we have a f is equal to see divided by C miners v Times F zero. So let me just rewrite this little differently as F is equal to one divided by one minus view or see times have zero. So I have that one minus view overseas, equal to the F zero, divided by F. Okay, which means that V is equal to see times one minus F zero divided by yes so V is equal to 343 m per second. This is the speed of sound times one minus F zero. That's 1400 hertz divided by F, which is 1600 hertz. So V is equal to 42.9 meters per second, which is the answer we were looking for, right?

Is the card approach you you will receive for sound off higher frequency than the frequent submitted by the car and the larder song. But when the brakes are applied in, the tradition has produced a frequency to suit by, you will be lower.

Alright in this problem, we actually have a two part problem here where we're kind of Children in our vehicle driving down the road, where we're siren or police car zooms past us and we hear the different frequencies. The first frequency we hear is 1300 hertz. And then the second frequency we hear is about 1280 hertz. Um That's part A will have to figure out. Well, we want to know how fast is the vehicle moving, How fast is that police car moving? We're gonna be looking for a velocity and then in part B. Well, we we pull over, we're good drivers, we pull over and then the ambulances coming up behind us. And as we're stopped, we hear the frequency of the ambulance being 1400 hertz and then 1200 hertz. Again, we want to know the actual frequency of the sound of the ambulance. So that's what part B will be. Well, for part A we have our equation kind of set up here, We have the velocity of of sound through normal air. We're just gonna assume where you're in normal air here. We have velocity one, which is how fast we're going, which is about 30 m per second. We have velocity to which is how fast the police vehicle is moving. And then we have the first frequency that we here and then the second frequency that we here as the police car passes, it's a two lane for four lane highway. So we're being nice and see if we did get over a little bit. We don't want to be messing around with all that. So here we go. For part A. We are going to plug in our numbers here. Again, the velocity of sound and air is about 300 40 three m per second plus how fast we're moving, which is 30 m per second. And I guess I should mention that we're dealing with the Doppler effect in this problem. Um We know the Doppler effect is that male noise or marrow and it's that that sound that we get when objects are moving past us or we are moving past objects that are making sound. It's actually quite cool actually. Um And then we again, we're looking for velocity to here. Our frequency number one is 1300 hertz. Equalling our second frequency, which is 12 80 hertz. At this point, we can just plug and chug and solve the equation for V two. If we add these numbers up top, we get somewhere around 300 somebody. Three over three already. Three plus our velocity squared. This is still being multiplied by 1300 going 12 80. All right now, we kind of pretend that there's an invisible one down here. We multiply across the top, multiply across the bottom. We get big numbers and that big number ends up being somewhere around or eight for nine zero zero over three for three plus velocity squared. Equalling now 12 80 for all of our math was up there. We know we need to multiply by the bottom here so it will cancel out down here. Which leaves us with. Okay, three, four really? Plus velocity squared? Oh sorry, not square. That's a subscript to um at this point then we can divide over our 12 80 which gets rid of this, which allows us to divide over here, which leaves us with three 70 mm or so Equalling three for three plus the velocity of the please vehicle subtract that over. We get somewhere around 33 meters per second. Again, double check the math there, see where we're rounding, see where the different decimal places are, but we should get about 33 m per second. For a part A. Again, we are dealing with the Doppler effect, so part B as I raise this over here. So for part B then we are now not moving. We're just kind of sitting there as the ambulances coming up behind us. And as the ambulance comes up behind us, we get to use our second equation, which is a little bit more simple to use. We have the frequency equaling the difference between the two frequencies over to. So it'll almost be the average there and for our second equation will have the frequency Equalling frequency one is 1400 minus 1200 all over to. And if we plug and chug this in our calculator, we get the frequency being 1300. So next time you're on the road and we have an ambulance and a police car coming up, maybe about your phone measure the decibels. Maybe we can get some some velocities and some frequencies going on and actually apply the store actual life.

As the ambulance approaches you, let's use the Doppler equation. Ex prime is equal to speed off sound in a The the Observer in this case is moving. But the sauce is the minus. The A velocity, the speed of the ambulance Times frequency off the source. So this is toward the observer and we know this to be 500 and 60 huts. The negative sign is because the source is moving toward the observer. What happens when the ambulance passes the observer and moves away? Well, now the shift in frequency, we call it f trying prime is just, you know something It over the thus, the a speed off the ambulance multiplied by the frequency of the ambulance. And we know this, as the ambulance pulls away is 480 huts. So it's obviously lower in the frequency off the sauce and it moves away. So if we solve this equation for F and use it, yeah, we get the expression as follows. That s trying is I see over the minus a B A is a constant. This feat of endurance is not changing, isn't exhilarating. Thus he a over be yes, double prime and with a bit more mathematics we get and we consult from the speed of the ambulance. E A is equal to speed of sound in a me too. It's time minus yes, that looked right. Every time is the apparent frequency as the evidence will swap jobs over Yes, double time is dependent frequency. As the evidence was away from the observed, all divided by next time thus gets double from and we know all these values. We know that the speed of sound in it its 340 feet your parent frequency. As the ambulance moves toward the observer, there's 560 hertz and 480 guts as it moves away. Over 560. Yes, 480. And this gives us speed off the ambulance. You do the calculation to be 26 0.4. You just a second


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