## Activity Based Physics Thinking Problems in Oscillations and Waves: |

1) A long wire is oscillating transversely so that its displacement
has the equation y(x,t) = A cos (k where A = 12 millimeters, k (a) With what speed is the wave moving down the wire? 2) In the four pictures labeled (A)-(D) below are shown snapshots of waves on a long, taut string. The dashed line shows a picture of a part of the string at the time t=0. The solid line is a picture at a time a little bit later. Each of these pictures looks the same at t=0, but the results differ because the parts of the string have different velocities at t=0 in each case.
For each of the four cases above, select one of the six patterns below as the correct velocity pattern to lead to the solid line displayed. (Note the arrows indicate mainly direction. Their lengths are scaled somewhat in proportion to their magnitude, but not strictly so.) 3) The graphs below may represent either a picture of the shape of a
wave on a string at a particular instant in time, t (a) a right going traveling wave For each of the following cases, decide what the wave is doing and choose one of the four letters (a)-(d). 3.1 Graph A is a graph of the string's shape and graph B is a graph
of the string's velocity.
4) A transverse wave pulse is traveling in the positive x direction along a long stretched string. The origin is taken at a point on the string which is far from the ends. The speed of the wave is v (a positive number). At time t=0, the displacement of the string is described by the function (a) Construct a graph that portrays the actual shape of the string at
t=0 for the case .
5) The picture below shows a snapshot of a piece of a wave at a time t=0. Make four copies of this picture and sketch what each pulse would look like at a slightly later time (a time small compared to the time it would take the pulse to move a distance equal to its own width but large enough to see a change in the shape of the string) for the following four cases:
On each picture draw arrows to show the velocity of the marked points at time t=0. 6) In the figure below are shown graphs which could represent properties of pulses on a stretched string. For the situation and the properties (a) - (e) below, select which graph provides the best representation of the given property. If none of the graphs are correct, write "none". Two pulses are started on a stretched string. At time ttheir peaks are separated by a distance
2_{0 }s. The distance between the pulses is much larger than their individual
widths. The pulses move on the string with a speed v
. The scales in the graphs are arbitrary and not necessarily the same.
_{0}(a) Which graph best represents the appearance of the string at time
(b) Which graph best represents the appearance of the string at a time ? (c) Which graph best represents the appearance of the string at a time ? (d) Which graph best represents the velocity of the string at a time ? (e) Which graph best represents the appearance of the string at a time where e is small compared to s/v? _{0
}
7) Discuss the physical meaning and content of the wave equation for
the motion of a string of mass density
8) A long taut spring is started at a time
(a) Draw a labeled graph showing the shape of the string at t=0.
9) In the figure below is shown a picture of a string at a time t Below are shown five graphs which could give the shape of the string
at the instant for which the velocities are displayed above. ( On your paper, place the letters A - E. Next to these letters, indicate for the graphs labeled by those letters, whether the string is moving as a (L) left-traveling wave 10) In the first section of the course, we have analyzed the motion of a mass on a spring and the motion of a taut string. Discuss these two systems, explaining similarities and differences, and give an equation of motion for each.
(a) Calculate the time t it will take the
peak of the pulse to reach the wall (to travel a distance s). 12) A guitar string having a mass density of m is stretched to a length L between its frets and is under a tension T.
13) The next set of four questions concern the motion of a pulse on a long taut string. We will choose our coordinate system so that when the string is at rest it is along the x axis of the coordinate system. We will take the positive direction of the x axis to be to the right on this page and the positive direction of the y axis to be up. Ignore gravity. A pulse is started on the string moving to the right. At a time t
For each of the items below, identify which figure above would look most like the graph of the quantity. (Take the positive axis as up.) If none of the figures look like you expect the graph to look, write N. 13.1. The graph of the y displacement of the spot of paint as a function
of time. 14) The next four problems concern the period of oscillation of a standing
wave on a string. Assume that the fundamental mode of oscillation of the
string has a period T 14.1 The mass density of the string is doubled. 15) Consider two physical systems:
16) The wave equation is often used to describe the transverse displacement of waves on a stretched spring. Explain the meaning of each of the elements of this equation with reference to the physical spring and discuss under what circumstances you expect it to be a good description.
The pulse is moving in the positive x direction (a) Sketch a graph showing the shape of the spring at a later time,
(b) Write an equation for the displacement of any portion of the spring at any time, y[x,t]. (c) Sketch a graph of the velocity of the piece of the spring at the position x = 2b as a function of time. 18) A physicist observes the motion of a plucked guitar string of length L. She proposes that the following function of position and time is a possible description of the displacement of the string:
(a) If the speed of transverse waves on the guitar string is w,
she wants or does it have to be some particular frequency? How do you know?
(b) If her equation is correct, which piece of the string moves the fastest? What is its maximum velocity? 19) A long elastic string is attached to a distant wall. A demonstrator holds the end of the string and quickly moves it up once and then back down to the original position, producing a pulse traveling towards the wall as shown. The demonstrator can make various changes before doing the experiment a second time. These include: 1) Moving his hand more quickly (but still only up and down once and
still by the same amount). For each of the following situations, which of the actions 1-8, (a) The demonstrator wants to produce a pulse that has the same height
as the original pulse but is 20) Consider the equation Let (a) Describe a physical situation represented by this equation. As part
of your description include a sketch and a written description. Indicate
what
22) A nylon guitar string has a linear mass density of 7.2 g/m and is
under a tension of 150 N. The fixed supports are 90 cm apart, The string
is vibrating in the standing wave pattern of a pure second harmonic, that
is, there are two nodes in addition to the endpoints. Calculate (a) the
speed, (b) the wavelength, and (c) the frequency of the component waves
whose superposition gives rise to this vibration. 23) Compare and contrast the behavior of (a) the mass of a mass-spring system oscillating in simple harmonic motion and (b) an element of a stretched string through which a traveling sinusoidal wave is passing. Discuss from the point of view of displacement, velocity, acceleration, and energy transfer. |

These problems written and collected by E. F. Redish. These problems
may be freely used in classrooms. They may be copied and cited in published
work if the *Activity Based Physics Thinking Problems in Physics site*
is mentioned and the URL given. Web page created and edited by K. A. Vick.

To contribute problems to this site, send them to redish@physics.umd.edu.

Go back to the Thinking Problems page

Go back to the Thinking Problems in Oscillations and Waves page

Maintained by
University of Maryland PERG

Comments and questions may be directed to
E. F. Redish

Last modified June 21, 2002