The picture above shows two waves, (a) and (b), both of which are on the same st

Question

The picture above shows two waves, (a) and (b), both of which are on the same string. What the string actually looks like is the superposition of these two waves.

(a) The displacement due to the (b) wave only is +4.0 cm at x = 35 cm and at x = 55 cm. The net displacement due to the two waves is larger at

x = 35 cm

x = 55 cm    

neither - the net displacement is the same at both these locations

(b) Briefly explain your answer above.

(c) The displacement due to the (a) wave only is +4.0 cm at x = 10 cm and at x = 50 cm. The net displacement due to the two waves is larger at

x = 10 cm

x = 50 cm    

neither - the net displacement is the same at both these locations

(d) At the instant in time shown in the picture, the largest net displacement due to the two waves is

less than 8.0 cm

exactly 8.0 cm    

more than 8.0 cm

Explanation / Answer

a)

Net displacement is larger at x = 55 cm

b)

since at x= 35 cm and x = 55 cm, (b ) has equal displacement of + 4 cm, so, net displacement of two waves will depend on the displacement of wave (a) at x = 35 cm and x= 55 cm,

so, at x = 35 cm, displacement of wave (a) is negative and x = 55 cm, displacement of wave (a) is positive, so,

after superimposition of two waves, net displacement is larger at x = 55 cm.

c)

Net displacement is same at x = 10 cm and x= 50 cm

d)

since at x= 10 cm and x = 50 cm, (a ) has equal displacement of + 4 cm, so, net displacement of two waves will depend on the displacement of wave (b) at x = 10 cm and x= 50 cm,

so, at x = 10 cm and x = 50 cm , displacement of wave (b) is same as equal to zero, so

net displacement, at (x = 10) = 4 + 0 = 4 cm

net displacement, at (x = 50) = 4 + 0 = 4 cm,

d)

at any instant of the given graph of (a) and (b) , since overlapping is not such like crust on crust or trough on trough, so largest net displacement should be less than (4+4 = 8 cm), so, less than 8 cm is the right answer

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