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Name That Harmonic: Strings - help7

Like any object, a string has a set of frequencies at which it naturally vibrates. When plucked, strummed, or somehow set into vibration, the string will vibrate at one of these frequencies. These frequencies are referred to as harmonics. The frequencies are related to one another by whole number ratios. For instance, the frequency of the 5th harmonic is 5 times larger than the first harmonic. And the frequency of the nth harmonic is n times larger than the frequency of the first harmonic.

There are three similar versions of this question. Here is one of those versions:
 

Version 1:

The fundamental or first harmonic frequency of a vibrating string is 80 Hz. The same string is capable of vibrating with several other standing wave patterns. Identify the standing wave pattern for the harmonic that has a frequency of 160 Hz.
 

Identifying the Harmonic Number
Every string (like a guitar string) has a set of frequencies with which it naturally vibrates. These frequencies are called harmonic frequencies and each is associated with a standing wave pattern. The lowest-pitched frequency in the set is called the first harmonic or fundamental frequency. All other frequencies are whole-number multiples of the fundamental frequency. The frequency values follow the equation fn = n•f1 where n is the harmonic number, f1 is the first harmonic (or fundamental) frequency, and fn is the frequency of the first harmonic. You can use the two given values for f1 and fn in this question to determine the harmonic number.


Selecting the Standing Wave Pattern
Standing wave patterns have nodes and antinodes. The nodes are points along the string that never move. The antinodes are points along the string that vibrate wildly between a high and a low position. The standing wave pattern for the first harmonic has one antinode. The second harmonic has two antinodes. The third harmonic has three antinodes. And so forth. So you need to tap through the choices until you find the pattern that has the correct number of antinodes.

Try these links to The Physics Classroom Tutorial for more help with the concept of standing wave patterns in strings:

Harmonics and Patterns

Mathematics of Standing Waves