Standing Waves on a String.pdf - Standing Waves on a String...

Standing Waves on a String
Equipment:
• Function Generator
• Mechanical Driver (It is a speaker with a string is tied to the post.)
• Table Clamp with a pulley on a post
• BNC to alligator clips cable
• Mass hanger
• Set of masses
Objectives:
• To find the linear mass density of the string using the relationship between the number of segments in
the standing wave and the tension in the string along with the frequency of oscillation of the string.
Introduction:
When a stretched string is plucked, it will vibrate in its fundamental mode in a single segment with nodes on
each end. If the string is driven at this fundamental frequency, a standing wave is formed. Standing waves also
form if the string is driven at any integer multiple of the fundamental frequency. These higher frequencies are
called the harmonics.
Each segment is equal to half a wavelength. In general for a given harmonic, the wavelength is given by:
?(?/2) = 𝐿
where L is the length of the stretched string and n is the number of vibrating segments in the string.
The linear mass density of the string can be directly measured by weighing a known length of the string. The
density is the mass of the string per unit length.
? = ?/𝐿
The linear mass density of the string can also be found by studying the relationship between the tension,
frequency, length of the string, and the number of segments in the standing wave. To derive this relationship,
the velocity of the wave is expressed in two ways.