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telo118 [61]
3 years ago
9

A pulse moving to the right along the x axis is represented by the function of

Physics
1 answer:
olasank [31]3 years ago
8 0

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

\displaystyle y(x,t)=\frac{2}{(x-3t)^2+1}

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

\displaystyle y(x,0)=\frac{2}{x^2+1}

The maximum value or the pulse amplitude occurs when the denominator has its minimum value, that is when x=0

\displaystyle A=y(0,0)=\frac{2}{0^2+1}=2

At t=1 second, the function is

\displaystyle y(x,1)=\frac{2}{(x-3)^2+1}

Again, the maximum value of the wave occurs at the minimum value of the denominator, or when

x-3=0 \rightarrow x=3

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

x-3t=0 \rightarrow x=3t

Taking the derivative with respect to t gives us the horizontal velocity:

x'=3\ cm/s

At t=2 seconds

\displaystyle y(x,2)=\frac{2}{(x-6)^2+1}

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

\displaystyle y(x,t)=\frac{2}{(x+3t)^2+1}

Then when t increases, the peak value moves to the left on the x-axis. The velocity would be

x'=-3\ cm/s

It means the wave is traveling to the left instead of to the right

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Answer:

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Explanation:

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At the beginning in this problem, we have:

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Later, the force does six times more work, so the work done now is

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And this work is done in half the time, so the new time is

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Substituting into the equation of the power, we find the new power produced:

P'=\frac{W'}{T'}=\frac{6W}{T/2}=12\frac{W}{T}=12P

So, 12 times more power.

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An apple falls out of a tree from a height of 2.3m. what is the impact speed of the apple
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Answer:

If we want to reach the planet PSR B1620-26 b, explain why we will need to make some big “wrinkle in time” discoveries or find ways to live much, much longer?

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If we want to reach the planet PSR B1620-26 b, explain why we will need to make some big “wrinkle in time” discoveries or find ways to live much, much longer?

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If we want to reach the planet PSR B1620-26 b, explain why we will need to make some big “wrinkle in time” discoveries or find ways to live much, much longer?

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2 years ago
Read 2 more answers
(a) Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is 3.85 108 m. Find
Goshia [24]

Answer:

It took 1.28 seconds to his voice to reach the Earth via radio waves.

Explanation:

The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities, that radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it.

The distribution of the radiation in the electromagnetic spectrum can also be given in wavelengths, but it is more frequent to work with it at frequencies, the highest being that of gamma rays, followed by X-rays, ultraviolet rays and the visible region , and those of lower frequencies, which correspond to infrared, microwave and radio waves.

Light propagates as electromagnetic wave in vacuum with a speed of 3x10^{8}m/s. Therefore, radio waves will have in vacuum the same speed.

Then, to know the time that it took for its voice, the next equation can be used:

c = \frac{d}{t}  (1)

Where c is the speed of light, d is the distance and t is the time.

Notice that t can be isolated from equation 1.

t = \frac{d}{c} (2)

t = \frac{3.85x10^{8} m}{3x10^{8}m/s}

t = 1.28s

Hence, it took 1.28 seconds to his voice to reach the Earth via radio waves.

7 0
3 years ago
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