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State whether the following functions ca...

State whether the following functions can represent wave motion ?

A. `y=sqrt((x-vt))`
B. `y=(x-vt)^2`
C. `y=A(x-vt)`
D. `y=A log (x+vt)^3`

A

`y=sqrt((x-vt))`

B

`y=(x-vt)^2`

C

`y=A(x-vt)`

D

`y=A log (x+vt)^3`

Text Solution

AI Generated Solution

To determine whether the given functions can represent wave motion, we need to analyze each function based on the characteristics of wave motion. Wave functions must be continuous, single-valued, harmonic (typically sinusoidal), and finite at every point. Let's evaluate each option step by step: ### Step 1: Analyze Function A **Function A:** \( y = \sqrt{x - vt} \) - **Single-valued:** For a given \( x \) and \( vt \), the square root function can yield two values (positive and negative) when \( x - vt \) is positive. For example, if \( x - vt = 1 \), then \( y \) can be \( +1 \) or \( -1 \). ...
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