Skip to main content

Learning Introductory Physics with Activities

Section 18.8 Making Standing Waves

Subsubsection Activities

Activity 18.8.1. Making Standing Waves.

Visit this website, hit the start button, and observe the behavior of the string.
(a)
Why do you think this is called a standing wave?
(b)
Identify the locations that remain always fixed (these are known as nodes) and the locations that oscillate most strongly (these are known as anti-nodes). Verify that the principle of superposition is accurate at these points.
(c)
With the wave reflecting from a free end in the simulation, click on Start, wait until the wave returns to its point of origin, and observe the new standing wave. What is different about it?

Activity 18.8.2. Fixed Ends.

Shown at the bottom of the page are three different standing waves that can be formed a string or spring, like the one in the experiment. Suppose you have such a string with length L and that both ends are fixed.
(a)
Identify all nodes and antinodes in the sketches.
(b)
For each sketch, determine the number of wavelengths that fit on the string. Use your answer to determine the wavelength \(\lambda\) in terms of the length of the string \(L\) and indicate it on your sketch.
(c)
Do you notice any patterns in the wavelengths? Can you come up with a general rule for all possible wavelengths?
(d)
Assuming you know the wave speed v, determine the frequencies \(f\) in terms of \(v\) and the length of the string \(L\text{.}\)
(e)
Sketch another wave on this string that has a higher frequency than the three waves shown.

Activity 18.8.3. The Banjo String.

A banjo string is \(0.7 \mathrm{~m}\) long and has a minimum (fundamental) frequency of \(392 \,athrm{~Hz}\) (G). Determine:
(a)
The wave speed along this string.
(b)
Three other frequencies at which this string can vibrate.
(c)
How long should you make the string to increase the minimum (fundamental) frequency to \(494 \mathrm{~Hz}\) (B)?

Activity 18.8.4. Fixed and Free Ends.

Consider a string with one end fixed but the other end is not fixed—instead, it is free to move back and forth.
(a)
Sketch the standing wave consistent with the ends of the string that has the largest wavelength.
(b)
Find the frequency of this standing wave.
(c)
Sketch at least two additional waves and find their wavelengths and frequencies.
(d)
Do you notice any patterns in the wavelengths? Can you come up with a general rule for all possible wavelengths?