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Question
Given below are some functions of x and t to represent the displacement of an elastic wave.
- y = 5 cos (4x) sin (20t)
- y = 4 sin (5x – t/2) + 3 cos (5x – t/2)
- y = 10 cos [(252 – 250) πt] cos [(252 + 250)πt]
- y = 100 cos (100πt + 0.5x)
State which of these represent
- a travelling wave along –x direction
- a stationary wave
- beats
- a travelling wave along +x direction.
Given reasons for your answers.
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Solution
- The equation y = 100 cos(100πt + 0.5x) is representing a travelling wave along the x-direction.
- The equation y = 5 cos(4x) sin(20t) represents a stationary wave because it contains sin, cos terms i.e., the combination of two progressive waves
- As the equation y = 10 cos[(252 – 250)πt] – cos[(252 + 250)πt] involving the sum and difference of two nearby frequencies 252 and 250 this equation represents beats formation.
- As the equation, y = 4 sin(5x – t/2) + 3 cos(5x – t/2) involves a negative sign with x, have if represents a travelling wave along the x-direction.
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