Studio Session 12

Mechanical Waves

A wave pulse is a disturbance that moves through a medium.  A periodic wave is a periodic disturbance that moves through a medium.  The medium itself goes nowhere.  The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change.  If the displacement of the individual atoms or molecules is perpendicular to the direction the wave is traveling, the wave is called a transverse wave.  If the displacement is parallel to the direction of travel the wave is called a longitudinal wave or a compression wave.

Waves can transport energy and information.  Examples of mechanical waves are water waves, sound waves, and seismic waves. All waves are described mathematically in terms of a wave function, and reflection, refraction and diffraction and interference a characteristic behaviors of all types of waves.

In this session you will study wave motion in one dimension only, to learn about several of these characteristic behaviors.  You will study the motion of waves on a string.

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  Address the points highlighted in blue.  Answer all questions.


Exploration

Use an on-line simulation from the University of Colorado PhET group to explore the behavior of waves on a string.
Link to the simulation: http://phet.colorado.edu/en/simulation/wave-on-a-string

(a)  Explore the interface.  Try the different controls and click "Help" to discover features you otherwise may miss.

(b)  Investigate the behavior of a wave pulse.

(c)  Investigate the behavior of a traveling wave.

  wave 1 wave 2 wave 3 wave 4 wave 5
amplitude A          
wavelength λ          
period T          
frequency f          
speed v          

(d)  Investigate the behavior of a standing wave.


Experiment

Standing waves of many different wavelengths can be produced on a string with two fixed ends, as long as an integral number of half wavelengths fit into the length of the string.  For a standing wave on a string of length L with two fixed ends

L = n(λ/2),  n = 1,2,3,...  .

For a string the speed of the waves is a function of the mass per unit length μ = m/L of the string and the tension F in the string.

v = √(F/μ).

In this experiment, waves on a string with two fixed ends will be generated by a string vibrator.  The waves will all have a frequency of 120 Hz.  Their wavelength is given by λ = v/f.  You will analyze video clips in which the string tension F is fixed and the length of the string is being varied.  You will measure the length of the string when the string supports a standing wave such that 1, 2, or 3 half wavelength of a wave fit into the length of the string.  Then 120 Hz is a natural frequency of the string and the vibrator drives the string into resonance.  The amplitude increases and the standing waves can easily be observed.

Procedure: (hints)

You will analyze three video clips, string_x.mp4, x = 1 - 3.  To play a video clip or to step through it frame-by-frame click the "Begin" button.  The "Video Analysis" web page will open.

Begin

string experimentIn the video clips the vibrator is mounted onto a rod which is fixed to the table with a clamp.  A pulley is mounted onto another rod on a movable stand.  One end of a string is attached to the vibrator.  The string is passed from the vibrator over the pulley and a mass is attached to its other end.  The string is level.

The string is a string with two fixed ends.  The amplitude of the vibrator arm is so small compared to the amplitude of the string at resonance, that the vibrator is very close to a node.  The other node is the top of the pulley.

vibrator

Clip f (Hz) L (m) λ (m) v = fλ (m/s) v2 (m/s)2 F (N)
String 1 120          
String 2 120          
String 3 120          

 

Data Analysis:

Calculate the measured wave speed v = fλ for each string.  For waves on a string we have F = μv2.  This tension is provided by a hanging mass, F = mg.  Calculate v2 and plot F versus v2.  Use Exce's trendline to find the best fitting straight line to this plot.  This slope of this line is equal to the mass per unit length of the string μ in kg/m?

Discuss:


Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.