what happens when standing wave goes from n=3 to n=5

A standing wave is a pattern which results from the interference of two or more waves traveling in the aforementioned medium.  All standing waves are characterized by positions forth the medium which are standing still.  Such positions are referred to equally nodes .  Standing waves are also characterized by antinodes .  These are positions along the medium where the particles oscillate almost their equilibrium position with maximum amplitude.  Continuing wave patterns are e'er characterized past an alternating blueprint of nodes and antinodes.

Transverse waves on a string

Continuing waves of many different wavelengths can be produced on a cord with two stock-still ends, as long as an integral number of half wavelengths fits into the length of the string.  For a continuing wave on a string of length Fifty with two fixed ends

Fifty = north(λ/2),  north = 1,2,3,... .

• Fundamental: L = λ/ii,  n = 1, 1/ii wavelength fits into the length of the string.
• Second harmonic: L = λ  due north = 2, 1 wavelength fits into the length of the string.
• Third harmonic: L = 3λ/two,  n = 3, 3/2 wavelengths fit into the length of the string.

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

In this lab, waves on a string with 2 stock-still ends will be generated by a string vibrator. The waves will  all have a frequency of 120 Hz. Their wavelength is given past λ = v/f.  Since the frequency is fixed, the wavelength of the waves can only be inverse by irresolute the speed of the waves.  Students volition 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.  So 120 Hz is a natural frequency of the string and the vibrator drives the cord into resonance.  The amplitude increases and the standing waves can easily be observed.

Summary:

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

Equipment needed:

• electrical string vibrator
• caster
• base and support rods and clamps
• mass hanger and mass set
• level
• meter stick

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Experiment:  Standing waves on a cord

• Mount the vibrator on a rod which is fixed to the tabular array with a clamp.  Mount the pulley onto another rod stock-still to the table with a clamp.  Pass a string from the vibrator over the pulley and adhere a mass hanger.  Make sure the string is level.  You lot now take a string with ii fixed ends.
  • The aamplitude of the vibrator arm is and so small compared to the amplitude of the string at resonance, that the vibrator is very close to a node.

    

• Open up an Excel spreadsheet and paste the table below into the spreadsheet

  	n	measured L (k)	λnorthward = 2L/n (1000)	speed vn = fλdue north (m/s)	hanging mass at resonance (kg)	measured F = mg (N)
  Fundamental: (due north = i)	1
  2d harmonic: (n = ii)	2
  Third Harmonic: (due north = 3)	iii

• Allow the length of the string from the vibrator to the peak of the pulley be somewhere betwixt 0.8 thousand and ane.2 1000.  Enter the length Fifty into the advisable cells of the spreadsheet.
• For your called length 50 use the spreadsheet to summate the wavelength λ_n = 2L/n then the speed 5_n = fλ_n = 2fL/n of the fundamental and second and third harmonic for f = 120 Hz.
• Turn on the vibrator.  Try to produce the primal continuing wave on the the string.  Accommodate the corporeality of mass hanging from the string until the cord is driven into resonance.  Enter the measured value for the hanging mass.  Calculate the measured force F = mg. (g = ix.8 m/s²)
• Repeat for the second and third harmonic and fill in the tabular array.

Information Analysis:

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

Discuss:

• Were you able to conspicuously identify the resonances?

• How exercise your values of μ obtained from the 3 measurements compare? In your opinion, are they equal within experimental uncertainties. If not, what exercise you call up can explain the differences?

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Open up Microsoft Word and prepare a short written report.

Proper name:
E-mail address:

Laboratory 1 Report

• Summarize the experiment.

• Show your table and comment on your results.

• Address the points highlighted in blue.  Answer all questions.

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Source: http://electron6.phys.utk.edu/phys250/Laboratories/standing_waves.htm

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