This'll question number 54 from Chapter 17 and this problem. We're given a 1.8 meter long tube and air temperature of 20 degrees Celsius. Were asked If I'm with the two will produce in the audible range if a The tomb is open at one end and B if it's open at both ends. So first thing. What is this audible range? Just as a reminder. The audible range of hearing frequency is 20 to 20,000 hertz. So that's the range will be looking for. And then I wanna hunt, wrote the equations that will be using. We need to find the speed of sound and air first, and then we'll be using the frequency equations. This is F equals envy. Over to l is when both ends are open and F equals and V over for l is when only one end is open. All right, so let's find this airspeed airspeed, uh, sound of speed and air, speed of speed, of sound and air. Excuse me 331 meters per second times the square root of 20 plus 2 73 over to 73. And that gives us a speed of 342 0.91 meters per second. All right, so now we have our speed. Let's go on to part a. So frequencies the two will produce in the audible range if it's open at one end, which is going to be n equals V over four of this equation. Okay, so first thing, we need to find the lowest range which we need to find out. If the low. If the resonance frequency would be setting this and equal toe, one is going to give us something in the lower range. So let's all for the resident's frequency one times 3 42.91 meters per second barn by four times 1.8 meters and that is going to give us a frequency 47.63 hurts. So that's the lowest frequency. That this that tube is going to produce of one end is open and that does fall in the range. So that's the lowest. And now we need to find the highest. So to do that, we can set our frequency as 20,000 the upper range of the audible range, and we can solve for N And what that will dio is that will be the exact, um, the exact number, Um, the exact end that would produce this frequency. And we can go down to the energy or value right below that to find what the actual frequency would be, Um, at that residence. So four times 1.8 meters per second. Excuse me, meters, not for a second meters. All right, so we most fly four times 1.8 over the other side. We divide by this speed of air, and that's going to give us an end equal to 419.93 OK, so that's our end that produces exactly 20,000 hurts. But to get the upper range, we're gonna lower this to the energy right below it, because that will give us a realistic frequency. So now we saw for that frequency, So and is gonna be 4 19 times divided by four times 1.8 meters. And that gives us a frequency of 19,955 hurts. And that is your range. Let's see your low waas 43 47.63 So there's a range if it's open at one end. So now we go to be we do the same process, but it's gonna be open at two ends, which was gonna be f equals and the over to l. All right, so it's all for the lowest frequency we could get and see if it's in the range. T o f equals one times 3 42 0.91 meters per second, divided by two times 1.8. And that gives us a frequency of hold on one second calculators of 95.25 It hurts. Okay, so that's gonna be our low. It does fall above 20 hertz, which is the audible range. And now we're gonna solve for the high the same way. So we plug in the upper range and we're gonna solve for end 3 40 2.91 and sulfur end. You get 209.96 and that is the exact number of, um, harmonics. Exact number. So now we go one energy blow that to find the realistic actual frequency that would fall 209 times well 3 42.91 meters per second over two times 1.8 meters, and that gives us a frequency of 19th i 1009 08 Hertz. So arrange here is 95 0.25 hertz to 19,000 908 turds, and that's the range if the tube is open at what?