Which of the following functions represent a stationary wave? Here a, b and c are constants:
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a
y=a cos (bx) sin (ct)
b
y=a sin (bx) cos (ct)
c
y=a sin (bx+ct)
d
y=a sin (bx+ct)+a sin (bx−ct)
answer is A.
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Detailed Solution
A stationary wave is characterized by a function of type y=f(t) g(x). Hence, choices (1) and (2) represent a stationary wave. Choice (4) is superposition of two oppositely travelling waves of the same amplitude and same frequency, which gives rise to a stationary wave. Hence choice (4) also represents a stationary wave.