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he equation of wave is $y = 5\sin (\dfrac{t}{{0.04}} - \dfrac{x}{4})$ where $y$ is in centimetre, $x$ is in centimetre and $t$ is in seconds. The maximum velocity of the particles of the medium is ?

Last updated date: 17th Jul 2024
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Hint: In order to solve this question, you must be aware about the concept of sinusoidal wave. All of the characteristics of the wave are contained in its wave function. A sine wave is a geometric waveform that oscillates (moves up, down or side-to-side) periodically. In other words, it is an s-shaped, smooth wave that oscillates above and below zero.

Complete step by step answer:
Equation of wave $y = 5\sin (\dfrac{t}{{0.04}} - \dfrac{x}{4})$
The standard equation of the wave in the given form is
$y = a\sin (\omega t - \dfrac{{2\pi x}}{\lambda })$
Comparing the given equation with the standard equation, we get
$a = 5$ and $\omega = \dfrac{1}{{0.04}} = 25$ and $\lambda = 8\pi $
${v_{\max }} = a\omega \\
\Rightarrow {v_{\max }}= 5 \times 25$
$\therefore {v_{\max }} = 1.25\dfrac{m}{s}$

Note: Waves on a string travel faster if you increase the tension of the string. Sound waves travel faster if you increase the temperature of the air. Changing the frequency or amplitude of the waves will not change the wave speed, since those are not changes to the properties of the medium.