A wave is described by the equation y = (1.0 mm) π ( x 2.0 cm - t 0.01 s ). Find the time period and the wavelength.

Correct answer: A. 20 ms , 4.0 cm The given wave equation is y = (1.0 mm) π ( x 2.0 cm - t 0.01 s ) Comparing this with the standard wave equation y = A (kx - ω t) , we get: k = (π)/(2.0) cm^ -1 ω = (π)/(0.01) s^ -1 Using the relation k = (2π)/(λ), we find the wavelength: (2π)/(λ) = (π)/(2.0) λ = 4.0 cm Using the relation ω = (2π)/(T), we find the time period: (2π)/(T) = (π)/(0.01) T = 0.02 s = 20 ms

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A wave is described by the equation y = (1.0 mm) π ( x 2.0 cm - t...

A wave is described by the equation

y = (1.0

\text{ mm}) \sin \pi

\left(\dfrac{x}{2.0 \text{ cm}} - \dfrac{t}{0.01 \text{ s}}\right).

Find the time period and the wavelength.

Options

A $20 \text{ ms}$ , $4.0 \text{ cm}$
B $10 \text{ ms}$ , $2.0 \text{ cm}$
C $40 \text{ ms}$ , $8.0 \text{ cm}$
D $0.01 \text{ s}$ , $2.0 \text{ cm}$

Correct answer

A. $20 \text{ ms}$ , $4.0 \text{ cm}$

Step-by-step solution

The given wave equation is

y = (1.0 \text{ mm}) \sin \pi \left(\dfrac{x}{2.0 \text{ cm}} - \dfrac{t}{0.01 \text{ s}}\right)<br><br>Comparing this with the standard wave equation

y = A \sin (kx - \omega t)

, we get:<br><br>

k =

\dfrac{\pi}{2.0} \text{ cm}^{-1}<br><br>

\omega =

\dfrac{\pi}{0.01} \text{ s}^{-1}<br><br>Using the relation

k =

\dfrac{2\pi}{\lambda}, we find the wavelength:<br><br>\dfrac{2\pi}{\lambda} = \dfrac{\pi}{2.0} \Rightarrow \lambda =

4.0 \text{ cm}

<br><br>Using the relation

\omega =

\dfrac{2\pi}{T}, we find the time period:<br><br>\dfrac{2\pi}{T} = \dfrac{\pi}{0.01} \Rightarrow

T = 0.02 \text{ s} = 20 \text{ ms}

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