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How long must a flute be in order to have a fundamental frequency of 262 Hz (this frequency corresponds to middle C on the evenly tempered chromatic scale) on a day when air temperature is $20.0^{\circ} C?$ It is open at both ends.

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Physics 101 Mechanics

Chapter 17

Physics of Hearing

Sound and Hearing

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

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offload is open on board dense, which means it's fundamental. Freak note must look something like this. That is the length off. The flute must correspond to half of it. Because if you notice this way, then goes on to continue like this on this is half a veil on. This is half of it. So l is Lambda too. So we want to find the length of the flute here on we can connect the Waveland who are frequency because we because we know the temperature off air, we can find the speed 20 degrees Celsius speed of the air is 3 43 meters per second by using the formula that we used earlier in the chapter at the speed is 3 31 times X squared off temperature in killing by 273. So using that formula, you don't see that it is equal to 3 40 And we also remember that the speed off like is equal to Lambda Kinds frequency. And from this equation we see that lambda is two times the length, So we substituted that frequency deigns to time stealing and that is it. It's a length is a little speed off the sound feed off some divided by two things the frequency. So that's 3 43 meters per second. Divided by 206. You do hoods times two so wanting. So it's always a good frak. Tous you look a unit's on DSI that you're getting the right numbers. I'm sorry you're getting the right units. It always makes sure that you are in the right direction. So in this scenario, noticed that Ah hurt is won by second. So we can cancel these two, which means our units will be in meters, which is good because building must be in meters. I know that we have this will simply plug our numbers into a calculator on We'll see that the link is equal to zero point 65 meters. I'm sorry. Yes, it's 0.66 meters. It's actually zero point 655 meters. But if you round up, you'll get this. But because we have three significant digits in the question will use 655 instead and that is it. In fact, this is actually how long fluids are. 65 centimeters is about the length of our normal food. There you have it

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