A tensioned string is a vibrating system. When you pull back the string and release it, the string tension accelerates the string back toward its equilibrium position, as the drawing shows.
The variables that affect the frequency of a vibrating string are the string tension, the string length, and the string’s mass per unit length. When the string is pulled back, the restoring force is equal to the sum of the two components of the tension that are perpendicular to the undisturbed string. The larger the tension, the larger the restoring force, the more rapidly the string will accelerate back toward the equilibrium position. The higher the tension, the higher the frequency, and, when the sound is heard, the higher the pitch.

Suppose you plucked a long and a short string. The drawing shows what happens. The component of the tension that is restoring the string to the equilibrium position is much higher for the shorter string. For the same amplitude, the shorter string experiences a larger restoring force. Consequently, its frequency will be correspondingly higher, as will the pitch it produces. The third variable is the mass per unit length of the string (although students do not investigate it in this activity). Take a look at piano strings or guitar strings. The bass strings of a piano are much more heavily wound than the midrange or treble strings. In a nylon-string guitar, the base strings are wound with metal wire, and the lower the string, the heavier the wire. The larger the mass per unit length of the string, the less it responds to the tension that pulls it back toward the equilibrium position. The larger the mass per unit length, the lower the frequency.
Standing waves form on the string in the same way as on the spring.

When the string in a musical instrument vibrates, it moves in a combination, or superposition, of many standing wave patterns. A guitarist can suppress certain of these standing waves to emphasize the remaining ones by making “chimes.” The technique is to simultaneously pluck the string and lightly tap it at the right spot for the particular chime. If the guitarist taps the string right in the middle, that suppresses the fundamental and all other odd harmonics with large amplitudes in the center of the string (the fundamental is the first harmonic).

Note: In the activity students find the wavelength of the fundamental from the length of the string. Since the activity does not introduce harmonics, the wavelength is called “the wavelength of the sound.”