Mastering Physics Solutions: Fundamental Wavelength and Frequency Ranking Task

Fundamental Wavelength and Frequency Ranking Task

Part A = (B,F) < (A,C,E) < D (increasing order)
Part B = (C,D,F) < (A, B) < E (increasing order)

Solution Below:

A combination work of art/musical instrument is illustrated. Six lengths of identical piano wire are hung from the same support, and masses are hung from the free end of each wire. Each wire is 1, 2, or 3 units long, and each supports 1, 2, or 4 units of mass. The mass of each wire is negligible compared to the total mass hanging from it. When a strong breeze blows, the wires vibrate and create an eerie sound.

Part A

Rank each wire-mass system on the basis of its fundamental wavelength.

The fundamental is proportional to the length of the wire:

λ = 2 * length

So the ranking (from shortest to longest wavelength) is:

(B,F) < (A,C,E) < D

(B,F) < (A,C,E) < D

Part B

Rank each wire-mass system on the basis of its wave speed.

Wave speed is proportional to tension, so in this case it’s proportional to the number of masses hanging on the wire. In order of increasing wave speed:

(C,D,F) < (A, B) < E

(C,D,F) < (A, B) < E

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