A standing wave is a pattern which results from the interference of two or more waves traveling in the same medium. All standing waves are characterized by positions along the medium which are standing still. Such positions are referred to as nodes. Standing waves are also characterized by antinodes. These are positions along the medium where the particles oscillate about their equilibrium position with maximum amplitude. Standing wave patterns are always characterized by an alternating pattern of nodes and antinodes.
Transverse waves on a string
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 fits 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.
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. Students 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.
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.
Experiment: Standing waves on a string
|n||measured L (m)||λn = 2L/n (m)||speed vn
|hanging mass at
F = mg (N)
|Fundamental: (n = 1)||1|
|Second harmonic: (n = 2)||2|
|Third Harmonic: (n = 3)||3|
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.
How do your values of μ obtained from the three measurements compare? In your opinion, are they equal within experimental uncertainties. If not, what do you think can explain the differences?
Open Microsoft Word and prepare a short report.
Summarize the experiment.
Show your table and comment on your results.
Address the points highlighted in blue. Answer all questions.