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Intro to Standing Waves

Consider the ...

Question

Consider the three waves, $z_{1}, z_{2}$ and $z_{3}$ as $z_{1} = A sin (k x - ω t), z_{2} = A sin (k x + ω t)$ and $z_{3} = A sin (k y - ω t)$ . 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_{2} + 2 z_{3}

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Solution

The correct option is A $z_{1} + z_{2}$
Stationary waves are formed by the superposition of two identical waves traveling in opposite directions along same direction.
$z_{1} = A sin (k x - ω t)$ $\to$ travel along $+ x$ axis.
$z_{2} = A sin (k x + ω t)$ $\to$ travel along $- x$ axis.
$z_{3} = A sin (k y - ω t)$ $\to$ travel along $+ y$ axis.
So, according to definition, $z_{1} + z_{2}$ represents the standing wave.

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Similar questions

Q. Consider the three waves

z_{1}, z_{2}

z_{3}

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?

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}

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}})

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 numbers such that

z_{2} \neq 1, a = | z_{1} |, b = | z_{2} |

c = | z_{3} |

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

. Then which of the following options is (are) CORRECT?

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Intro to Standing Waves

Standard XII Physics

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