Post on 18-Aug-2015
PULSE SPEED ON A HANGING STRING
A young physics student at UBC had finished his homework
early in the morning and realized he had the rest of the
afternoon free. Unfortunately, he was going through some self-
esteem issues and wanted to spend the afternoon with
someone who found him attractive. He ventured campus in
hopes of finding a life long companion that would reassure him
of his good looks. He came across a vendor who was selling
magical lamps. The young physics student thought it would be
a good investment because he could just wish for someone to
find him attractive.
PROBLEM
The vendor sold the student the lamp but the genie that
appeared refused to grant him his wish without proof that the
student understood the concept of pulse speed on a hanging
string. The genie hung the 5kg lamp to the ceiling with a string.
The genie then told the student that the string had a linear mass
density of 30g/m and a length of 10m. The genie then generated a
pulse at the lower end of the string and asked, “What is the speed
of the pulse at the lower end, middle, and at the top of the string?
Also, where is the pulse speed greatest and why?”
KNOWN QUANTITIES
Linear mass density of the string, u
30.0g/m = 0.0300kg/m
Mass of the lamp, M
5kg
Length of the String L,
10m
SOLUTION
Tension in a string at any point is a result of the weight of
the hanging mass as well as the weight of string below the
point. If we allow x to be the height at a given point from the
bottom of the string, the total weight under point x is equal
to Mg + (uxg), which is equivalent to tension at that height.
The following equation is wave speed, v(x), at a height x:
RESULT
The boy explained to the genie the concept behind his results.
The pulse speeds up as a result of the tension in the string
increasing with height, therefore the pulse speed is greatest
at the top of the string. This concept applies to any string of
nonzero linear mass density that is hanging vertically. When a
pulse is generated at the bottom, the pulse moves upwards
and the speed increases.