00:01
Hi there, so for this problem we have a flute that assembles her flute in a room where the speed of sound is given, and that speed of sound is 342 meters per second.
00:19
When she placed the node a, it is in perfect tone with a 440 hertz tuning force.
00:29
So we are given a frequency for 140 hearse.
00:38
After a few minutes, the air inside her flute has warmed to where this speed of sound is now a value.
00:48
Let's call this the value prime, and that is equal to 344 meters per second.
00:59
Now, for part a of this problem, we are asked about, how many bits per second will she hear if she now plates the knot a as the tuning 4 is sounded? okay, so for this part of the problem, first of all, we need to determine the wavelength.
01:28
In the wavelength, we know that we can determine that quantity by dividing the speed by the frequency, where b is the speed of the wave and f is the frequency.
01:42
Thus, the wavelength of the sum wave of the node a that we are given that we know is 440 hertz and the speed that is 342 meters per second.
02:00
So from this ratio, we obtain a wavelength of, well, 342 meters per second divided by 4402 meters per second, divided by 4404.
02:15
From this we obtain a value of 0 .7773 meters.
02:27
Now, since the earth inside the node was warm after a while, the wave will have a new frequency, which well we can call as, let's call it f prime, the frequency prime.
02:47
So that will be the speed prime divided by the wavelength.
02:53
So that will be the value that we are given, which is 300, let me just verify this about 344 meters per second divided by the wavelength that we just determined, which is 0 point this value right here.
03:12
So using our calculator, we obtain a value of, 442 56 hearse so now let's just so now we just need to take the difference between these two values and we will obtain the number of bits per second so that will be so let's call the number of bits and this is equal to 442 .56 hz minus the initial value that is 440 hertz.
04:13
So from this we obtain a value of 2 .56 hertz.
04:21
So that means 2 .56 beats per second.
04:32
So that's a solution for part a of this problem.
04:36
Now for par b, we are asked about how far does she need to stand the turning joint or of her flute to be in tune with the turning fork? so in this case, we know that the frequency now of the standing wave models is just, let's call this the frequency m is equal to.
05:11
To n times the speed divided by two times length l, where n is a positive integer and l is the open tooth length...