Which of the following wave(s) can produce standing wave when superimposed with $y = A sin (ω t + k x)$ :

A sin (ω t - k x + 30^{o})

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A cos (ω t - k x)

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A sin (k x - ω t)

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None of these

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Solution

The correct options are
A $A sin (ω t - k x + 30^{o})$
B $A cos (ω t - k x)$
For standing wave to be formed the interfering waves must have same amplitude, same frequency and opposite direction of travelling. These are satisfied by options A and B.

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Similar questions

Which of the following two wave equations can form stationary wave?

(i) $Y = A s i n (ω t - k x)$

(ii) $Y = A c o s (ω t - k x)$

(iii) $Y = A s i n (ω t + k x)$

(iv) $Y = A c o s (ω t + k x)$

y_{1} = A s i n (ω t - k x) a n d y_{2} = A s i n (ω t + k x)

y = a cos (ω t - k x)

x = 0

y = a s i n (ω t - k x)

y = a c o s (ω t - k x)

y = A sin (ω t - k x)

y = A sin (ω t + k x)

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