a) y = 5 cos (4x) sin (20t)

b) y = 4 sin (5x-t/2) + 3 cos (5x-t/2)

c) y = 10 cos [(252-250)πt] cos [(252+250) πt]

d) y = 100 cos (100 πt + 0.5x)

State which of these represent

a) a traveling wave along -x direction

b) a stationary wave

c) beats

d) a traveling wave along +x direction

Give reasons for your answers

Answer:

a) When a wave travels in the direction of (-x), it must have +kx, which is calculated as:

d) y = 100 cos (100 πt + 0.5x)

b) In case of a stationary wave, we have:

a) y = 5 cos (4x) sin (20t)

c) When beats are involved

c) y = 10 cos [(252-250)πt] cos [(252+250) πt]

d) a travelling wave along +x direction is

b) y = 4 sin (5x-t/2) + 3 cos (5x-t/2)