Two waves are propagating on the same very long string. A generator at one end o
ID: 1700850 • Letter: T
Question
Two waves are propagating on the same very long string. A generator at one end of the string creates wave 1, given by the followingequation.y = (8.0 cm)cos p/2[(4.0m-1)x + (9.0s-1)t]
A generator at the other end of the string creates wave 2, given bythis equation.
y = (8.0 cm)cos p/2[(4.0m-1)x - (9.0s-1)t]
For x > or = 0, what are the locations of the nodes having the smallest(x1), second smallest (x2),and third smallest (x3) values of x.
x1---------m
x2------ m
x3---------m
Repeat for the antinodes with the smallest values of x.
x1-----------m
x2----------m
x3----------m
Explanation / Answer
y1 = 8.0 cos p/2[4.0x + 9.0t]
y2 = 8.0 cos p/2[4.0x - 9.0t]
Resulting Wave can be obtained by adding these two waves
y = y1 + y2
=> y = 8.0 cos p/2[4.0x + 9.0t] + 8.0 cos p/2[4.0x - 9.0t]
=> y = 8.0 { cos p/2[4.0x + 9.0t] + cos p/2[4.0x - 9.0t] }
=> y = 8.0 { 2*cos p/2(4.0x)*cos p/2(9.0t) } {since cosA + cosB = 2*cos( (A+B)/2 ) * cos( (A-B)/2 )}
Let's take the snapshot at t=0
=> y = 16.0 cos p/2(4.0x)
For nodes y = 0
=> y = 16.0 cos p/2(4.0x) = 0
=> cos p/2(4.0x) = 0
=> p/2(4.0x) = /2 , 3/2 , 5/2
=> x1 , x2 , x3 = /4p , 3/4p , 5/4p
For antinodes |y| = maximum
=> |y| = |16.0 cos p/2(4.0x)| = 16.0
=> p/2(4.0x) = 0 , , 2
=> x1 , x2 , x3 = 0 , /4p , 2/4p
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.