00:01
Hello student, in this portion we are given that two loud speakers a and b which emit sinusoid waves in phase of frequency 68 earth and we are given that they are placed 12 meters apart and now we have to determine the points of constructive and destructive interference between the two speakers when we are standing along the line joining the speakers.
00:26
So first of all, we would have to calculate the wavelength for the emitted frequency and that is.
00:31
Would be equal to the speed of sound divided by the frequency and substituting the values a wavelength noted by lambda would be equal to the speed of sound which is equal to 344 meters per second and divided by the frequency which is equal to given in the question as 68 per so upon calculating this arc wavelength that is noted by lambda is coming out to the 0 .5 meters now as they have calculated the wavelength we would utilize this in order to calculate the positions of constructive interference and destructive interference.
01:06
So first of all for constructive interference as we know that for constructive interference are the part difference could be equal to for constructive interference you write for constructive interference the part difference that is divided by delta x must be equal to n multiplied by the lambda that is where n is any integer are part difference would be equal n multiplied by lambda as for example we have two speakers we have two speakers this is a speaker a and at that this location we are placing a speaker 2 which is at a distance of 12 meters from speaker a suppose we are standing in between we are given that we are standing in between at point c so the part difference at point c for example assuming the distance from a speaker would be x so the distance from the loud speaker would be equal to 12 minus x.
02:09
So the part difference at point c would be equal to the 12 minus x, that is the distance from speaker b, minus of distance from speaker a, that is equal to minus x.
02:22
So this is the part difference and that would be equal to n multiplied by lambda.
02:26
So upon putting the value of lambda, our equation for part difference is equal to 12 minus 2x, is equal to n multiplied by 0 .5 so upon rearranging on both sides or we can say multiplying by 0 .5 both sides we get the equation which is equal to x the x which is equal to 6 minus 0 .25 times of where n is any integer so with changing the integer with changing the value of n we would obtain certain point in the in the line joining the speaker in this line joining the speaker where we would get the constructive and destructive interference so in this case for constructive interference when n is equal to for example when n is equal to one upon putting n is equal to one our part difference would be equal to or we can say the distance of x that is the distance of point c from here would be equal to 5 minus 6 minus 0 .25 times of 1 that would be equal to 0 .5 .75 meter.
03:41
So this is the position of constructive interfills.
03:46
Similarly, putting n is equal to 2, we would get 5 .50 meters.
03:52
Similarly, putting n is equal to 3, this is for n is equal to 2.
03:56
Now putting n is equal to 3, we would get a position that is 5 .25 meters.
04:02
And similarly, the pattern continues, that would be equal to, last would be equal to 0.
04:08
0 .25 meters upon putting the values of n.
04:11
So these all points are of constructive interference.
04:14
So we can state that the constructive interference is located at constructive interference is located at for example from 0 .25 meters from at question 0 .25 meters 0 .50 meters this we are just stating 0 .25 to each term or 0 .75 meters similarly to the pattern 11 .25 meters 11 .50 meters 11 .15 meters and 11 .75 meters.
04:59
So these all are place positions of constructive interference these all are positions of constructive interference.
05:08
Now in the next part of the question, this was the first part of the question and in the next part of the question we have to determine that what would be the distance moved by the person if he was standing in it initially he was standing in between the speakers we are given that this is a speaker a and this is our speaker b and in between the he was standing at position c which is at a distance of six meters from both ends so we are given that he standing from six meters from both ends and now how much distance he would move towards speaker loud speaker b in order to reach the destructive interference.
05:50
So let's start this part.
05:52
Now first of all, the relation for destructive interference, the condition for destructive interference, that would be equal to for destructive interference.
06:05
The condition is that the part difference, again denoted by delta x, and that would be equal to 2n plus 1 divided by, multiplied by lambda, divided by 2.
06:19
So this is the condition for the destructive interference...