Problem 5: Two transverse waves travel along the same taut string. Wave 1 is described by y,(x, t) = A sin(kx - wt), while wave 2 is described by y2(x, t) = A sin(kx + wt + q). The phases (arguments of the sines) are in radians, as usual, and A = 3.6 cm and o = 0.65n rad. Part (a) Choose the answer that correctly describes the waves' directions of travel. MultipleChoice : 1) Due to the o term in the phase of wave 2, it does not travel. Wave 1 travels in the positive x-direction. 2) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction. 3) Both waves travel in the negative x direction. 4) There is not enough in: 5) Both waves travel in the positive x-direction. 6) Wave 1 travels in the negative x-direction, while wave 2 travels in the positive x-direction. 7) Due to the ø term in the phase of wave 2, it does not travel. Wave 1 travels in the negative x-direction. nation. Part (b) What form do the wave functions take at the position x = 0? MultipleChoice : 1) y1 = A, y2 = 0 2) y1 = A sin(-wt), y2 = A sin(wt + p) 3) y1 = A cos(-wt), y2 = A cos(wt + g) 4) y1 = A sin(k - wt), y2 = A sin(k + wt + ø) 5) y1 = 0, y2 = 0 6) There is not enough information. 7) yı = A sin(-wt), y2 = A cos(wt) B) y1 = A sin(-wt), y2 = A sin(wt) 9) y1 = 0, y2 = A a-B sin 2 a+B Part (c) Use the trigonometric identity sin a+sin ß=2cos- displacement of the string at the positic.. . SchematicChoice : to find the correct function of time for the total y(t) = 2 sin- cos (wt + y(t) = 2A sin cos (wt + y(t) = 2A cos sin (wt + y(t) = 2A sin sin (wt + ) y(t) = A sin cos (wt + 2) y(t) = 2A sin o cos(2wt + «) cos (ut + y(t) = 2A cos
Problem 5: Two transverse waves travel along the same taut string. Wave 1 is described by y,(x, t) = A sin(kx - wt), while wave 2 is described by y2(x, t) = A sin(kx + wt + q). The phases (arguments of the sines) are in radians, as usual, and A = 3.6 cm and o = 0.65n rad. Part (a) Choose the answer that correctly describes the waves' directions of travel. MultipleChoice : 1) Due to the o term in the phase of wave 2, it does not travel. Wave 1 travels in the positive x-direction. 2) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction. 3) Both waves travel in the negative x direction. 4) There is not enough in: 5) Both waves travel in the positive x-direction. 6) Wave 1 travels in the negative x-direction, while wave 2 travels in the positive x-direction. 7) Due to the ø term in the phase of wave 2, it does not travel. Wave 1 travels in the negative x-direction. nation. Part (b) What form do the wave functions take at the position x = 0? MultipleChoice : 1) y1 = A, y2 = 0 2) y1 = A sin(-wt), y2 = A sin(wt + p) 3) y1 = A cos(-wt), y2 = A cos(wt + g) 4) y1 = A sin(k - wt), y2 = A sin(k + wt + ø) 5) y1 = 0, y2 = 0 6) There is not enough information. 7) yı = A sin(-wt), y2 = A cos(wt) B) y1 = A sin(-wt), y2 = A sin(wt) 9) y1 = 0, y2 = A a-B sin 2 a+B Part (c) Use the trigonometric identity sin a+sin ß=2cos- displacement of the string at the positic.. . SchematicChoice : to find the correct function of time for the total y(t) = 2 sin- cos (wt + y(t) = 2A sin cos (wt + y(t) = 2A cos sin (wt + y(t) = 2A sin sin (wt + ) y(t) = A sin cos (wt + 2) y(t) = 2A sin o cos(2wt + «) cos (ut + y(t) = 2A cos
Related questions
Question
Transcribed Image Text:Problem 5: Two transverse waves travel along the same taut string. Wave 1 is described by y,(x, t) = A sin(kx -
wt), while wave 2 is described by y2(x, t) = A sin(kx + wt + Q). The phases (arguments of the sines) are in
radians, as usual, and A = 3.6 cm and o = 0.65A rad.
Part (a) Choose the answer that correctly describes the waves' directions of travel.
MultipleChoice :
1) Due to the o term in the phase of wave 2, it does not travel. Wave 1 travels in the positive x-direction.
2) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
3) Both waves travel in the negative x direction.
4) There is not enough information.
5) Both waves travel in the positive x-direction.
6) Wave 1 travels in the negative x-direction, while wave 2 travels in the positive x-direction.
7) Due to the o term in the phase of wave 2, it does not travel. Wave 1 travels in the negative x-direction.
Part (b) What form do the wave functions take at the position x = 0?
MultipleChoice :
1) y1 = A, y2 = 0
2) y1 = A sin(-wt), y2 = A sin(wt + p)
3) y1 = A cos(-wt), y2 = A cos(wt + 4)
4) y1 = A sin(k - wt), y2 = A sin(k + wt + ø)
5) y1 = 0, y2 = 0
6) There is not enough information.
7) y1 = A sin(-wt), y2 = A cos(wt)
8) y1 = A sin(-wt), y2 = A sin(wt)
9) y1 = 0, y2 = A
Part (c) Use the trigonometric identity sin a+sin ß=2cosPsit
a-B
a+B
to find the correct function of time for the total
sin
2
displacement of the string at the positic.. .
SchematicChoice :
y(t) = 2 sin-
cos ( wt +
y(t) = 2A sin-
- cos (wt +
) y(t) = 2A cos, sin (wt +
= 2A sin sin (wt +) y(t) = A sin-
(at +) yt)
y(t)
%3D
= 2A sin o cos(2wt + 4)
y(t)
cos (wt +
= 2A cos
- cos
Part (d) With A = 3.6 cm and o = 0.65T; rad, calculate the total displacement of the string, in centimeters, at the position x =
0 at time t = 0.
Numeric : A numeric value is expected and not an expression.
y(0) =
Part (e) If, instead, you are given o = 0, what will be the total displacement of the string at the position x = 0 as function of
time, t.
MultipleChoice :
1) The displacement will vary between -2A and 2A at a rate given by the period, 27/w.
2) The displacement will be y = 0 for all t.
3) The displacement will be y = A sin(4) for all t.
4) There is not enough information.
5) The displacement will be y = 2A for all t.
6) The displacement will be y = A for all t.
7) The displacement will vary between -A and A at a rate given by the period, 27/w
Expert Solution
Step 1
Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. If you want the remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
