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.

Equipment needed:

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.

(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 lab, 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.  Since the frequency is fixed, the wavelength of the waves can only be changed by changing the speed of the waves.  You will adjust the tension in the string until 1, 2, or 3 half wavelength of a wave with f = 120 Hz 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.

Summary:

Given: f = 120 Hz.
Measure: tension F, for λ = L/2, L, 2L/3
Calculate: the mass per unit length μ of the string, using v = λf,  μ = F/v2.

Procedure:

n measured L (m) λn = 2L/n (m) speed vn = fλn
(m/s)
hanging mass at
resonance (kg)
measured
F = mg (N)
Fundamental: (n = 1) 1          
Second harmonic: (n = 2) 2          
Third Harmonic: (n = 3) 3          

Data Analysis:

Calculate the mass per unit length μ of the string using μ = F/v2.  Average the values obtained from your three measurements and estimate the uncertainty in this average value.

Discuss:


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