A wave propagates along the positive x -direction with a speed of 20 m s^ -1 . The amplitude of the wave is 0.20 cm and the wavelength is 2.0 cm . Which of the following is a possible wave equation that describes this

Correct answer: C. y = (0.20 cm) [(π cm^ -1 )x - (2π × 10^3 s^ -1 )t] The amplitude of the wave is A = 0.20 cm . The wavelength is λ = 2.0 cm . The wave number k is given by k = (2π)/(λ) = 2π 2.0 cm = π cm^ -1 . The wave speed is v = 20 m s^ -1 = 2000 cm s^ -1 . The angular frequency ω is given by ω = kv = (π cm^ -1 )(2000 cm s^ -1 ) = 2π × 10^3 s^ -1 . For a wave propagating in the positive x -direction, the equation is of the form y = A (kx - ω t) . Substituting the values, we get y = (0.20 cm) [(π cm^ -1 )x - (2π × 10^3 s^ -1 )t] .

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 propagates along the positive x -direction with a speed of...

A wave propagates along the positive

x

-direction with a speed of

20 \text{ m s}^{-1}

. The amplitude of the wave is

0.20 \text{ cm}

and the wavelength is

2.0 \text{ cm}

. Which of the following is a possible wave equation that describes this wave?

Options

A $y = (0.20 \text{ cm}) \sin[(2\pi \text{ cm}^{-1})x - (\pi \times 10^3 \text{ s}^{-1})t]$
B $y = (0.20 \text{ cm}) \sin[(2\pi \text{ cm}^{-1})x + (\pi \times 10^3 \text{ s}^{-1})t]$
C $y = (0.20 \text{ cm}) \sin[(\pi \text{ cm}^{-1})x - (2\pi \times 10^3 \text{ s}^{-1})t]$
D $y = (0.20 \text{ cm}) \sin[(\pi \text{ cm}^{-1})x + (2\pi \times 10^3 \text{ s}^{-1})t]$

Correct answer

C. $y = (0.20 \text{ cm}) \sin[(\pi \text{ cm}^{-1})x - (2\pi \times 10^3 \text{ s}^{-1})t]$

Step-by-step solution

The amplitude of the wave is

A = 0.20 \text{ cm}

.

The wavelength is

\lambda = 2.0 \text{ cm}

.

The wave number

k

is given by

k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{2.0 \text{ cm}} = \pi \text{ cm}^{-1}

.

The wave speed is

v = 20 \text{ m s}^{-1} = 2000 \text{ cm s}^{-1}

.

The angular frequency

\omega

is given by

\omega = kv = (\pi \text{ cm}^{-1})(2000 \text{ cm s}^{-1}) = 2\pi \times 10^3 \text{ s}^{-1}

.

For a wave propagating in the positive

x

-direction, the equation is of the form

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

.

Substituting the values, we get

y = (0.20 \text{ cm}) \sin[(\pi \text{ cm}^{-1})x - (2\pi \times 10^3 \text{ s}^{-1})t]

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