Transverse waves on an elastic spring

Physics 122 4/16/2017 What happens when a a short pulse is “flicked” down a long, taut spring? It keeps its shape but gets smaller the farther it goes. It keeps its shape and stays the same size. It changes shape, but stays about the same size. It changes shape, and gets smaller. I have no clue. NEXUS/Physics Clicker Questions Prof. E. F. Redish

What happens? Physics 122 4/16/2017 NEXUS/Physics Clicker Questions Prof. E. F. Redish

Physics 122 4/16/2017 If this is the space-graph (photo at an instant of time) what does the time-graph look like for the bead marked with a red arrow? y x Pulse moving to the right NEXUS/Physics Clicker Questions The students should be sketching possibilities and you draw on those. But be prepared to put up your own. The standard error is to draw it looking like the space graph instead of flipped horizontally. This is a good opportunity to bring them to think about the motion of the pulse and what it means for the bits of the spring in time. Choice One Choice Two Choice Three Choice Four Choice Five Choice Six Choice Seven Choice Eight Prof. E. F. Redish

Describing the motion of the beads Physics 122 4/16/2017 Describing the motion of the beads Pulse moving to the right y x NEXUS/Physics Clicker Questions Sketch vertical arrows showing how each bead is moving as the pulse moves from the first position to the second. vy x Prof. E. F. Redish

A pulse is started on the string moving to the right A pulse is started on the string moving to the right. At a time t0 a photograph of the string would look like figure 1 below. A point on the string to the right of the pulse is marked by a spot of paint. (x is horizontal and right, y is vertical and up) Which graph would look most like a graph of the y displacement of the spot as a function of time? NEXUS/Physics Clicker Questions 7 None of these

A pulse is started on the string moving to the right A pulse is started on the string moving to the right. At a time t0 a photograph of the string would look like figure 1 below. A point on the string to the right of the pulse is marked by a spot of paint. (x is horizontal and right, y is vertical and up) Which graph would look most like a graph of the x velocity of the spot as a function of time? NEXUS/Physics Clicker Questions 7 None of these

A pulse is started on the string moving to the right A pulse is started on the string moving to the right. At a time t0 a photograph of the string would look like figure 1 below. A point on the string to the right of the pulse is marked by a spot of paint. (x is horizontal and right, y is vertical and up) Which graph would look most like a graph of the y velocity of the spot as a function of time? NEXUS/Physics Clicker Questions 7 None of these

A pulse is started on the string moving to the right A pulse is started on the string moving to the right. At a time t0 a photograph of the string would look like figure 1 below. A point on the string to the right of the pulse is marked by a spot of paint. (x is horizontal and right, y is vertical and up) Which graph would look most like a graph of the y force on the spot as a function of time? NEXUS/Physics Clicker Questions 7 None of these

What Controls the Speed of the Pulse on a Spring? Physics 122 4/16/2017 What Controls the Speed of the Pulse on a Spring? To make the pulse go to the wall faster Move your hand up and down more quickly (but by the same amount). Move your hand up and down more slowly (but by the same amount). Move your hand up and down a larger distance in the same time. Move your hand up and down a smaller distance in the same time. Use a heavier string of the same length under the same tension. Use a string of the same density but decrease the tension. Use a string of the same density but increase the tension. Put more force into the wave, Put less force into the wave. NEXUS/Physics Clicker Questions Prof. E. F. Redish

Below is a snapshot of a piece of an elastic spring on which a pulse is traveling.   Each square of the grid represents 1 cm.   In a video of the motion of the pulse, the pulse is observed to move a distance of 2 cm in 0.04 seconds. Three pieces of tape are attached to the spring.   They are marked by small circles in the figure and are labeled A , B , and C . Graph the velocity of each of the 3 pieces of tape as the pulse moves past them. (Take this instant as t = 0) NEXUS/Physics Clicker Questions

Which goes with which? Graph I Graph II Graph III NEXUS/Physics Clicker Questions Graph III

How do waves combine? We know how one pulse moves. What happens when we get two pulses on top of each other? NEXUS/Physics Clicker Questions ?

What happens if they overlap perfectly? NEXUS/Physics Clicker Questions Most students will predict that they will cancel but will then assume that it then stops, failing to think about the fact that the bits of the string may still have velocity. ?

What happens when they would have passed each other if the other hadn’t been there? 1. (Bounce off) NEXUS/Physics Clicker Questions (Pass through) 2. 3. (Cancel) 4. Other

? 1. NEXUS/Physics Clicker Questions 2. 3. Other

How about on the same side? NEXUS/Physics Clicker Questions

NEXUS/Physics Clicker Questions

An elastic string (modeled as a series of beads) driven by a wheel driving one of the beads up and down sinusoidally. . The driving wheel has generated a traveling wave of amplitude 10 cm moving to the right. (The string continues on for a long way to the right as indicated by its going “out the window.”) The figure shows t = 0, when the green bead marked “II” is passing through its equilibrium point. Which of the graphs could serve as the graph of the vertical displacement of bead II as a function of time? NEXUS/Physics Clicker Questions

An elastic string (modeled as a series of beads) driven by a wheel driving one of the beads up and down sinusoidally. . The driving wheel has generated a traveling wave of amplitude 10 cm moving to the right. (The string continues on for a long way to the right as indicated by its going “out the window.”) The figure shows t = 0, when the green bead marked “II” is passing through its equilibrium point. Which of the graphs could serve as a graph of the vertical displacement of bead III as a function of time? NEXUS/Physics Clicker Questions

An elastic string (modeled as a series of beads) driven by a wheel driving one of the beads up and down sinusoidally. . The driving wheel has generated a traveling wave of amplitude 10 cm moving to the right. (The string continues on for a long way to the right as indicated by its going “out the window.”) The figure shows t = 0, when the green bead marked “II” is passing through its equilibrium point. Which of the graphs could serve as a graph of the vertical displacement of the elastic string at the time t = 0 as a function of position? NEXUS/Physics Clicker Questions

Graph A is a graph of the string's shape and graph B is a graph of the string's velocity. Is the wave on the string:  a right going traveling wave  a left going traveling wave  a part of a standing wave growing in amplitude at time t1  a part of a standing wave shrinking in amplitude at time t1 none of the above  you can’t tell from the info given.  NEXUS/Physics Clicker Questions

Graph A is a graph of both the string's shape and the string's velocity. Is the wave on the string:  a right going traveling wave  a left going traveling wave  a part of a standing wave growing in amplitude at time t1  a part of a standing wave shrinking in amplitude at time t1 none of the above  you can’t tell from the info given.  NEXUS/Physics Clicker Questions

Graph B is a graph of the string's shape and graph A is a graph of the string's velocity. Is the wave on the string:  a right going traveling wave  a left going traveling wave  a part of a standing wave growing in amplitude at time t1  a part of a standing wave shrinking in amplitude at time t1 none of the above  you can’t tell from the info given.  NEXUS/Physics Clicker Questions

This is the state of the PhET wave-on-a-string simulation when the string is very long so reflection can be ignored. What is the speed of the wave (assuming that the frequency is given in cycles/min? NEXUS/Physics Clicker Questions

For what frequencies will we generate a large (resonant) standing wave if we drive it with a small amplitude? NEXUS/Physics Clicker Questions

If we start our beaded string off in a sinusoidal shape If we start our beaded string off in a sinusoidal shape y(x) = A sin(πx/L) it will oscillate with a frequency f0. If we start it out with a shape y(x) = A sin(2πx/L) with what frequency will it oscillate? f0 2f0 f0/2 Something else NEXUS/Physics Clicker Questions

If we start our beaded string off in a sinusoidal shape If we start our beaded string off in a sinusoidal shape y(x) = A sin(πx/L) it will oscillate with a frequency f0. If we start it out with a complex shape (shown) will it ever repeat itself? If yes, with what frequency? No f0 2f0 f0/2 Something else NEXUS/Physics Clicker Questions

A standing wave increasing in amplitude In the figure below is shown a picture of a string at a time t1. The pieces of the string are each moving with velocities indicated by arrows. (Vertical displacements are small and don't show up in the picture.) if the shape of the string at time t1 is that shown below (displacement magnified by X100) then the motion of the string is Left traveling wave Right traveling wave A standing wave increasing in amplitude A standing wave decreasing in amplitude None of these. NEXUS/Physics Clicker Questions

A standing wave increasing in amplitude In the figure below is shown a picture of a string at a time t1. The pieces of the string are each moving with velocities indicated by arrows. (Vertical displacements are small and don't show up in the picture.) if the shape of the string at time t1 is that shown below (displacement magnified by X100) then the motion of the string is Left traveling wave Right traveling wave A standing wave increasing in amplitude A standing wave decreasing in amplitude None of these. NEXUS/Physics Clicker Questions

A standing wave increasing in amplitude In the figure below is shown a picture of a string at a time t1. The pieces of the string are each moving with velocities indicated by arrows. (Vertical displacements are small and don't show up in the picture.) if the shape of the string at time t1 is that shown below (displacement magnified by X100) then the motion of the string is Left traveling wave Right traveling wave A standing wave increasing in amplitude A standing wave decreasing in amplitude None of these. NEXUS/Physics Clicker Questions