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Expression for Standing Waves

Consider the ...

Question

Consider the three waves $z_{1}, z_{2}$ and $z_{3}$ as
$z_{1} = A s i n (k x - ω t)$
$z_{2} = A s i n (k x + ω t)$
$z_{3} = A s i n (k y + ω t)$
Which of the following represents a standing wave?

A

z_{1} + z_{2}

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B

z_{2} + z_{3}

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C

z_{3} + z_{1}

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D

z_{1} + z_{2} + z_{3}

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Solution

The correct option is A $z_{1} + z_{2}$
Standing waves are produced when two waves propagate in opposite direction.
As $z_{1}$ and $z_{2}$ are propagating in +ve x-axis and -ve x-axis.
So, $z_{1} + z_{2}$ will represent a standing wave.

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Similar questions

Q. Consider the three waves,

z_{1}, z_{2}

z_{3}

z_{1} = A sin (k x - ω t), z_{2} = A sin (k x + ω t)

z_{3} = A sin (k y - ω t)

. Which of the following represents a standing wave?

Q. Consider the three waves,

z_{1}, z_{2}

z_{3}

z_{1} = A sin (k x - ω t), z_{2} = A sin (k x + ω t)

z_{3} = A sin (k y - ω t)

. Which of the following represents a standing wave?

z_{1}

z_{2}

z_{3}

are three distinct complex numbers such that

\frac{1}{∣ z_{1} - z_{2} ∣} = \frac{3}{∣ z_{2} - z_{3} ∣} = \frac{5}{∣ z_{1} - z_{3} ∣}

, then the value of

\frac{1}{z_{1} - z_{2}} + \frac{9}{z_{2} - z_{3}} + \frac{25}{z_{3} - z_{1}}

z_{1}, z_{2}, z_{3}

represent the vertices of an equilateral triangle such that

| z_{1} | = | z_{2} | = | z_{3} |

z_{1}, z_{2}, z_{3}

be three non-zero complex number, such that

z_{2} \neq z_{1}, a = | z_{1} |, b = | z_{2} | a n d c = | z_{3} |

∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣ = 0

(\frac{z_{3}}{z_{2}})

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