How Do You Calculate Amplitude and Wave Velocity from a Wave Equation?

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The wave equation provided is y = 30 sin(30πt + 0.03πx), indicating that the amplitude of the wave is 30 cm. To calculate the wave velocity, one can use the wave number and angular frequency derived from the equation, leading to a wave velocity of 1 m/s. The amplitude of particle velocity can be calculated using the formula for particle velocity amplitude, which involves the angular frequency and the wave's amplitude. The discussion also raises questions about the nature of the particles in the wave and what physically moves as the wave propagates. Understanding these concepts is essential for solving the problem accurately.
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Homework Statement


My professor has given us a pset with this problem:

A plane mechanical wave is represented by the equation y = 30 sin(30\pi t + 0.03 \pi x)
Where y is measured in cm, x is measured in metres and time (t) is measured in seconds. Find
(i)amplitude of particle velocity
(ii)wave-velocity


Homework Equations





The Attempt at a Solution


While I know how to find (ii), I don't know how to find out (i). Can somebody please tell me ?
 
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chomsky said:

Homework Statement


My professor has given us a pset with this problem:

A plane mechanical wave is represented by the equation y = 30 sin(30\pi t + 0.03 \pi x)
Where y is measured in cm, x is measured in metres and time (t) is measured in seconds. Find
(i)amplitude of particle velocity
(ii)wave-velocity


Homework Equations




The Attempt at a Solution


While I know how to find (ii), I don't know how to find out (i). Can somebody please tell me ?
What are the particles to which the question is referring? What actually moves when the wave passes a location?
 

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