00:01
So let's start with the problem.
00:01
There are two waves on a string and the wave functions are written as y1 equal to 3 cos 4x minus 1 .6 t and we have y2 as 4 .0 sign.
00:16
Okay, 4 .0 sign.
00:18
This is what? 5 .0x minus 2 .0 t.
00:26
Okay.
00:27
Where x and y are in centimeters and t.
00:30
And it is in second.
00:31
No issues so you have to find the value of y1 okay y1 plus y2 okay so at three points we have been given three points okay so let me just write what are the conditions given x equal to 1 .00 and t is equal to 1 .00 b x is equal to 1 .00 and t is equal to 0 in 5 000 at c where x equal to 0 .50 and t is equal to 0 we just have to substitute these particular values into the equation and just solve it okay so let's start okay let's start with the a part okay so a part we have x equal to one centimeter and time is equal to one second okay so you will just do y1 plus y2 okay so just write them uh 3 cos okay right 3 costs 4 .0 x minus 1 .6 t okay uh plus 4 plus what we have is 4 sign 5 .0 x minus 2 .0 t okay so now just substitute the bias wherever you have x put x equal to 1 wherever you have t put t is equal to 1 okay so this becomes uh 3 cos okay uh 4 .0 0 .0 into 1, okay, minus 1 .6 into 1, okay? and over here we have 4 sign, okay? 5 .0 into 1 minus 2 into 1.
02:14
Okay, see, i'm not writing the whole 0 .00, but when you write in your problem, when you write the solution, kindly put 0 wherever it is given, okay? so this is 3 costs, okay? 3 costs and inside what will happen 4 minus 1 .6 what is 4 minus 1 .6 it will be 2 .4 okay and here it is 4 sign okay 5 minus 5 minus 2 will be what 3 okay sign 3 okay just remember these values are in radiance okay so just use your calculator and just find this will be minus 2 .212 plus the other value will be 0 .5645.
03:01
You can use your calculator to find the values.
03:04
This will be equal to minus 6 .47 centimeter.
03:08
Okay.
03:09
This is the solution for a part.
03:11
I will have to please pause the video and write it down or take a screen shot.
03:15
Because in order to move on to the next part, i need to have, i need to wrap this earlier part.
03:23
Okay so let's move on to the b part i'm sorry for that what have you heard is this part of the google assistant i'm sorry for that uh so let's move on to the b part okay so in b part we are having x equal to 1 okay no issues and time is equal to 0 .5 so be careful with the calculations we just have to do y is equal to y1 plus y 2 okay you know so write y okay y 1 you write 3 cos 4 .0 x minus 1 .6 t and again y2 that is 4 sign 5 .0 x minus 2 .0 t okay so for x you have to put 1 and for t you have to put 0 .5 so just substitute 3 cost 4 into 0 into 1 minus 1 .6 into this time it's 0 .5 so be careful and 4 sign okay here 5 .0 into 1 and 2 into t t is 0 .5 okay okay so so this is 3 cos, okay, this will be 4 itself and 1 .6 into 0 .5.
04:35
That means it will be half.
04:37
So this will be 0 .8, okay? and over here, 4 sign 5 into 1 is 5 and 2 into 0 .5 will be 1.
04:46
Okay, so this will be 3 cos and what will be here? this will be 3 .2.
04:52
Okay and over here this will be 4 sign 4 okay so when you calculate this comes out as minus 2 .995 plus this will be minus of 3 .027 okay so just hold on for a second just let me just once again cross check this okay where is sign this is changed to sign 4 will be how much? same 4 is minus 0 .4 and times 4...