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Q.

A sine wave has an amplitude A and wavelength . Let V be the wave velocity and v be the maximum velocity of a particle in the medium. Which of the following options is correct?


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a

V = v, if A =

b

V = v, if A =

c

V = v, if

d

V = v, if{"mathml":"<math class="image_resized" style="width:51px;height:36px"><span style="font-family: 

answer is D.

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Detailed Solution

Concept- When a particle's velocity in a medium reaches its maximum, that velocity will be equal to the sum of the wave's amplitude and angular frequency. The wavelength and frequency of a wave are used to express its velocity. We should be able to calculate the requisite wave amplitude by equating the two relations.
Formula used: The wave's velocity is determined by,Question Image where Question Image is the wave's frequency, and Question Image is the wave's wavelength.
A wave's angular frequency may be calculated using,Question Image where Question Image is the wave's frequency.
Step 1: Give the wave's parameters in a list.
A sine wave with amplitude A and wavelength is presented Question Image as seen in the following figure.
Question ImageLet Question Image be the sine wave's frequency and be its angular frequency.
Additionally, the wave's speed is stated to be Question Image while the particle's maximum speed in the propagation medium is stated to be v.
Step 2: Indicate the relationship between the maximum particle velocity in the medium and the wave's velocity.
Given the particle's maximum speed in the medium, v, we have Question Image - (1)
The wave's velocity is now stated as Question Image (2)
Let's assume that the two speeds are equivalent, or Question ImageEquations (1) and (2) are substituted in (3) to get,Question Image but as Question Image we have Question ImageQuestion Image or Question Image.
Thus Question Image only if Question Image.
Hence, the correct answer. is option 4.
 
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