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The Bay of Fundy, Nova Scotia, has the highest tides in the world. Assume in midocean and at the mouth of the bay the Moon's gravity gradient and the Earth's rotation make the water surface oscillate with an amplitude of a few centimeters and a period of $12 \mathrm{h} 24 \mathrm{min}$. At the head of the bay, the amplitude is several meters. Assume the bay has a length of $210 \mathrm{km}$ and a uniform depth of $36.1 \mathrm{m}$. The speed of long-wavelength water waves is given by $v=\sqrt{g d}$, where $d$ is the water's depth. Argue for or against the proposition that the tide is magnified by standing-wave resonance.

$12.4 \mathrm{h} \approx 12 \mathrm{h} 24 \mathrm{min}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 14

Superposition and Standing Waves

Periodic Motion

Mechanical Waves

Electromagnetic Waves

Simon Fraser University

Hope College

University of Sheffield

McMaster University

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Hi, everybody. So, for this one, um, we need to argue are for or against the proposition that the tide is nine fired by the standing wave. Um, resonance. So we need to find the speed of water as we have speed of water as g divide about times D. And that's the grab These in 9.81 meters per second squared and the old things were routed times on the distance, which was 36.1 years, which is what was given to us for the Nova Scotia uniformed death so that he's been depth and we get 18 a point eight meters per second. OK, so now we need a wavelength of the water wave, and that is gonna be Landau over four. Okay. And again, that's just has to dio where, um, sine waves. And that's a terrible sign has to do with sine waves. And, um, this one is just the fourth of it. Okay. And, um um, you guessed race this, We don't need it. You do, Erica. And because of that, um, to me, land a before and then it. So you're lamp lambda is ableto four of the O, which is gonna be four times two tied at times. Time to three nurturers. Okay, Which equals 8 40 times 10 to 3. Nurse. Okay. And so we have our t equals one over. Frequency and frequency is been equal to be over Lambda. So that means you're t is gonna equal Teoh, uh, lambda over velocity and we get eight 40 times 10 to 3 meters, divided by the velocity that we found above 18 point year for eight meters per second. And then we get 4.47 times, 10 to the fourth seconds. And if you want to convert this two hours, we have one hour over three, 66 seconds and we get 12 points for one hours. Okay? And so now what we can dio is it's giving us, um for this. It says that centimeter period is 12 hours with 24 minutes. So what we have here is 12 hours, people. Full hours. Plus, we separate the 0.41 that we have here hours and we're income for that little bit. Two minutes, minutes, hours. Okay. And with this wind up getting in at 12 hours and 24 minutes and This is just using everything they gave us in the problem. And so this does agree that with the period of the wiener expectations of initial high tide is amplitude of the residence. Okay, guys, and let me just make that 60 just a little bit better for everybody. Okay? Thank you, guys.

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