A wave traveling along a string in the + x-direction is given by y1 (x, t) = A cos (wt – Bx), where...

Question

A wave traveling along a string in the + x-direction is given by y1 (x, t) = A cos (wt – Bx), where x = 0 is the end of the string, which is tied rigidly to a wall, as shown in Fig XXXXXXXXXXP1.6). When wave y1 (x, t) arrives at the wall, a reflected wave y2 (x, t) is generated. Hence, at any location on the string, the vertical displacement ys will be the sum of the incident and reflected waves: ys (x, t) = y1 (x, t) + y2(x, t).
(a)Write down an expression for y2(x, t), keeping in mind its direction of travel and the fact that the end of the string cannot move.
(b)Generate plots of y1 (x, t), y2 (x, t) and ys (x, t versus x over the range - 2?

Robert · Accepted Answer

1(x; t) = Acos(ωt�βx);
where x = 0 is the end of the string, which is tied rigidly to a wall, as shown in
Fig. 1-21 (P1.6). When wave y1(x; t) arrives at the wall, a reflected wave y2(x; t) is
generated. Hence, at any location on the string, the vertical displacement ys will be
the sum of the incident and reflected waves:
ys(x; t) = y1(x; t)+y2(x; t):
(a) Write down an expression for y2(x; t), keeping in mind its direction of travel
and the fact that the end of the string cannot move.
(b) Generate plots of y1(x; t), y2(x; t) and ys(x; t) versus x over the range
�2λ� x � 0 at ωt = π=4 and at ωt = π=2.
x
x = 0
Incident Wave
y
2(x; t) was caused by wave y1(x; t), the two waves must have the
same angular frequency ω, and since y2(x; t) is traveling on the same string as y1(x; t),
the two waves must have the same phase constant β. Hence,

A wave traveling along a string in the + x-direction is given by y1 (x, t) = A cos (wt – Bx), where x = 0 is the end of the string, which is tied rigidly to a wall, as shown in Fig XXXXXXXXXXP1.6)....

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment