A wave travelling on a string has the equation y = (0.10 mm) [(31.4 m^ -1 )x + (314 s^ -1 )t] . Determine the wave speed, the wavelength and the frequency of the wave.

Correct answer: D. 10 m s^ -1 , 20 cm , 50 Hz Comparing the given wave equation y = (0.10 mm) [(31.4 m^ -1 )x + (314 s^ -1 )t] with the standard wave equation y = A (kx + ω t) , we get: k = 31.4 m^ -1 and ω = 314 s^ -1 The wave speed is given by v = (ω)/(k) v = (314)/(31.4) = 10 m s^ -1 The wavelength is given by λ = (2π)/(k) λ = (2 × 3.14)/(31.4) = 0.2 m = 20 cm The frequency is given by f = (ω)/(2π) f = (314)/(2 × 3.14) = 50 Hz Thus, the wave speed is 10 m s^ -1 , wavelength is 20 cm and frequency is 50 Hz .

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 travelling on a string has the equation y = (0.10 mm) [(31.4...

A wave travelling on a string has the equation

y = (0.10 \text{ mm}) \sin[(31.4 \text{ m}^{-1})x + (314 \text{ s}^{-1})t]

. Determine the wave speed, the wavelength and the frequency of the wave.

Options

A $10 \text{ m s}^{-1}$ , $10 \text{ cm}$ , $100 \text{ Hz}$
B $5 \text{ m s}^{-1}$ , $40 \text{ cm}$ , $25 \text{ Hz}$
C $20 \text{ m s}^{-1}$ , $20 \text{ cm}$ , $50 \text{ Hz}$
D $10 \text{ m s}^{-1}$ , $20 \text{ cm}$ , $50 \text{ Hz}$

Correct answer

D. $10 \text{ m s}^{-1}$ , $20 \text{ cm}$ , $50 \text{ Hz}$

Step-by-step solution

Comparing the given wave equation

y = (0.10 \text{ mm}) \sin[(31.4 \text{ m}^{-1})x + (314 \text{ s}^{-1})t]

with the standard wave equation

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

, we get:

k = 31.4 \text{ m}^{-1}

and

\omega = 314 \text{ s}^{-1}

The wave speed is given by

v = \dfrac{\omega}{k}

v = \dfrac{314}{31.4} = 10 \text{ m s}^{-1}

The wavelength is given by

\lambda = \dfrac{2\pi}{k}

\lambda = \dfrac{2 \times 3.14}{31.4} = 0.2 \text{ m} = 20 \text{ cm}

The frequency is given by

f = \dfrac{\omega}{2\pi}

f = \dfrac{314}{2 \times 3.14} = 50 \text{ Hz}

Thus, the wave speed is

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

, wavelength is

20 \text{ cm}

and frequency is

50 \text{ Hz}

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