Answer:
<em>(a) Peak=2 cm, velocity= 3 cm/s (to the right)</em>
<em>(b) Peak= 2 cm, velocity= -3 cm/s (to the left)</em>
Explanation:
<u>Pulse Movement</u>
The function of a moving wave is given by
where x,y are measured in cm and t in seconds.
Please check the graph shown in the image provided below. It shows the waveform at two different times, t=0 sec and t=1 sec. The peak value is displaced by 3 cm when t varies by 1 second. It shows a velocity of 3 m/s.
(a) For a given time, say t=0 the expression for the pulse is
The maximum value or the pulse amplitude occurs when the denominator has its minimum value, that is when x=0
At t=1 second, the function is
Again, the maximum value of the wave occurs at the minimum value of the denominator, or when
Note the peak has moved 3 cm to the right when t increased by 1 second, this gives us a horizontal velocity of 3 cm/s.
We can corroborate for the general case knowing the peak value moves to the right at the point where
Taking the derivative with respect to t gives us the horizontal velocity:
At t=2 seconds
The amplitude and velocity are the same as determined before. The graph shown in the figure attached shows the pulse waves at t=0 and t=1
b) If the function was
Then when t increases, the peak value moves to the left on the x-axis. The velocity would be
It means the wave is traveling to the left instead of to the right