Find the distance this spot travels in one period.

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The discussion revolves around calculating the distance a marked spot on a rope travels during one complete oscillation of a transverse wave. The user initially used the equation for vertical position, which does not account for the total distance traveled. It was clarified that the spot moves up and down, and the total distance in one period is four times the amplitude, leading to a distance of 0.4 meters. The user also noted that the distance between crests is 2 meters, but this is separate from the distance the spot travels vertically. Understanding the difference between vertical position and total distance traveled is crucial for solving the problem.
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Ive been trying this problem for awhile now and I seem to not get it.

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 2.5s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1m. The frequency at which the crests pass a given point in space is 0.4 Hz. The distance between the two adjacent crests on the wave is 2m.

a) There is a blue spot drawn onto the rope with a magic marker. Find the distance this spot travels in one period.

I have tried using the equation y(t)=Asin(2*pi*f*t)
which is 0.1m*sin(2*pi*.4*2.5) = .0109 m and I got this wrong. I am not sure where I did go wrong and was wondering if anyone can help me. Thanks.
 
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justneedhelp81 said:
Ive been trying this problem for awhile now and I seem to not get it.

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 2.5s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1m. The frequency at which the crests pass a given point in space is 0.4 Hz. The distance between the two adjacent crests on the wave is 2m.

a) There is a blue spot drawn onto the rope with a magic marker. Find the distance this spot travels in one period.

I have tried using the equation y(t)=Asin(2*pi*f*t)
which is 0.1m*sin(2*pi*.4*2.5) = .0109 m and I got this wrong. I am not sure where I did go wrong and was wondering if anyone can help me. Thanks.

This equation gives the vertical position and since the point is moving up and down, calculating the position will not give the distance travelled. (I could move 20 meters to the right and then come back and my position will not have changed but the distance traveled will be 40 meters).

You should just visualize it. Let's say that the point is initially at the very top. Then as the wave passes it will move down for a while and eventually start moving up again. In terms of the amplitude A, what distance does it travel in one period?

Pat
 
crust to crust would be 2m, the one that i calculated, (velocity/frequency)
and in one period does it travel half the distance of amplitude?
 
.1m x 4 = .4m, i think i get it now
 

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