Question

A wave is represented by y=0.25x10^-3 sin (0.025x-500t),
where y, t, x are in meter respectively.

calculate=>

a) amplitude
b) Time period
c) angular velocity
d) wave length
e) speed
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Answer 1

Given:

A wave is represented by:

$\boxed{y = 0.25 \times {10}^{ - 3} \sin\bigg(0.025x - 500t \bigg)}$

where y, t, x are in meter respectively.

To find:

Value of :

• Amplitude
• Time period
• Angular frequency
• Wavelength
• Speed

Calculation:

Amplitude is the maximum displacement of the medium particles during propagation of the wave.

$y = 0.25 \times {10}^{ - 3} \sin\bigg(0.025x - 500t \bigg)$

• For amplitude, value of sin should be be max.

$\implies \: y_{max} = 0.25 \times {10}^{ - 3} \times \bigg(1\bigg)$

$\implies \: y_{max} = 0.25 \times {10}^{ - 3} \: m$

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Comparing the given equation with s standard equation of a wave :

$y = a \sin( kx - \omega t)$

We get ,

• $\omega$ = 500 Hz.
• k = 0.025

$\therefore \: angular \: freq. = \omega = 500 \: hz$

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$\therefore \: T = \dfrac{2\pi}{ \omega}$

$\implies \: T = \dfrac{2\pi}{500}$

$\implies \: T = 0.012 \: sec$

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$\therefore \: \lambda = \dfrac{2\pi}{k}$

$\implies \: \lambda = \dfrac{2\pi}{0.025}$

$\implies \: \lambda = \dfrac{2000\pi}{25}$

$\implies \: \lambda = 251.32 \: m$

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$\therefore \: v = f \times \lambda$

$\implies \: v = \dfrac{ \omega}{2\pi} \times \dfrac{2\pi}{k}$

$\implies \: v = \dfrac{ \omega}{k}$

$\implies \: v = \dfrac{500}{0.025}$

$\implies \: v = \dfrac{500 \times 1000}{25}$

$\implies \: v = 2 \times {10}^{5 } \: m {s}^{ - 1}$

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