Part 1: Setting up a Standing Wave

Investigation 15D: Resonance and Standing Waves

A standing wave is a wave that has been trapped between two boundaries, such as the fixed ends of an elastic string. Because standing waves persist for long periods of time they make an excellent example for investigating wavelength and frequency.

Part 1: Setting up a standing wave

1.  Launch the interactive simulation of a vibrating string driven by an oscillator.

2.  Change the oscillation frequency until you create a standing wave.

3.  Change the frequency to see different standing wave patterns with different numbers of nodes and antinodes.

Questions

a.  Do the standing waves appear at all frequencies or just specific ones? Explain this using the idea of resonance.

b.  Describe the role of reflection and interference in creating standing waves.

c.  Sketch two or three different standing wave patterns and indicate the wavelength of each.

Part 2: Relationship between wavelength and frequency

1.  Adjust the frequency until you get the largest amplitude standing wave you can that has a single node between its fixed ends. This is the second harmonic because there are two antinodes.

2.  Using the measuring scale, estimate the wavelength of the standing wave and record its wavelength and frequency.

3.  Adjust the frequency to find the standing waves from the first through the eighth harmonics and record the wavelength and frequency of each.

Table 1: Wavelength and frequency

Questions

a.  What is the relationship between frequency and wavelength? State it with a mathematical formula.

b.  What units does the product of frequency × wavelength have? What is the interpretation of this quantity?

c.  How could you control the frequency of a vibrating object through its wavelength? Describe at least two applications of this principle.

d.  Going further: What happens to the standing wave frequencies if you quadruple the tension in the string? What happens to the standing wave frequencies if you quadruple the mass per unit length of the string?

What do these results imply about the speed of waves in the string?

e.  Listen to the sound produced by the vibrating string. When you increase the tension in the string, does the pitch rise or fall? When you increase the mass of the string, does the pitch rise or fall? Can you relate this to playing an instrument?

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