SATHEE: Waves - Result Question 12

Waves - Result Question 12

12. The equation for a transverse wave travelling along the positive $x$ -axis with amplitude $0.2 m$ , velocity $v = 360 m s^{- 1}$ and wavelength $λ = 60 m$ can be written as

[2002]

(a) $y = 0.2 \sin [2 π (6 t - \frac{x}{60})]$

(b) $y = 0.2 \sin [π (6 t + \frac{x}{60})]$

(d) $y = 0.2 \sin [2 π (6 t + \frac{x}{60})]$

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Answer:

Correct Answer: 12. (a)

Solution:

(a) As we know that, velocity $v = n λ$

$\Rightarrow$ frequency, $n = \frac{v}{λ} = \frac{360}{60} = 6$

Amplitude, $a = 0.2$

For a wave travelling along positive $x$ -axis

$y = a \sin (ω t - k x)$

$= a \sin (2 π n t - \frac{2 π x}{λ})$

$= a \sin 2 π (n t - \frac{x}{λ}) = 0.2 \sin 2 π (6 t - \frac{x}{60})$

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Waves - Result Question 12

12. The equation for a transverse wave travelling along the positive x-axis with amplitude 0.2m, velocity v=360ms−1 and wavelength λ=60m can be written as

Answer:

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12. The equation for a transverse wave travelling along the positive $x$ -axis with amplitude $0.2 m$ , velocity $v = 360 m s^{- 1}$ and wavelength $λ = 60 m$ can be written as