Question 345: Waves

Question

The displacement of a wave is given by $y=0.002 \sin (100 t+x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

Accepted Answer

To analyze the given wave equation $ y = 0.002 \sin (100t + x) $, we compare it with the general wave form $ y = a \sin(\omega t + kx) $.
From this comparison, we identify:
$ \omega = 100 \, 	ext{rad/s} $
$ k = 1 \, 	ext{rad/m} $
$ a = 0.002 \, 	ext{m} $
The frequency $ n $ of the wave is calculated as follows:
$ n = \frac{\omega}{2\pi} = \frac{100}{2\pi} = \frac{50}{\pi} \, 	ext{Hz} $
The velocity $ v $ of the wave can be found using:
$ v = \frac{\omega}{k} = \frac{100}{1} = 100 \, 	ext{m/s} $
Also, the relationship between $ k $ and the wavelength $ \lambda $ is given by:
$ k = \frac{2\pi}{\lambda} $
Solving for $ \lambda $, we have:
$ \lambda = \frac{2\pi}{k} = 2\pi \, 	ext{m} $
Thus, this represents a wave that is traveling with a velocity of $ 100 \, 	ext{m/s} $ in the negative x-direction, as suggested by the positive $ kx $ term which indicates a negative direction in the wave propagation.

Answer

of wavelength one metre

Answer

travelling with a velocity of $100 \mathrm{~m} / \mathrm{s}$ in the negative $x$-direction

Answer

of frequency $\left(\frac{100}{\pi}\right) \mathrm{Hz}$

Answer

travelling with a velocity of $\left(\frac{50}{\pi}\right) \mathrm{m} / \mathrm{s}$ in the positive x -direction

Waves

The displacement of a wave is given by y=0.002 \sin (100 t+x) where ' x 'and ' y ' are in metre and ' t ' is in second. This represents a wave

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