WAVES

By Michael Lasaleta 39607122

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:

EVALUATING

At x=0, x= 5 and x=10

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.