# Physics, 9, wavelength, instruments vibrations?

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A combination work of art/musical instrument is illustrated. (http://session.masteringphysics.com/problemAsset/1… Six pieces of identical piano wire (cut to different lengths) 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.

largest to smallest

Part B

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

Rank from largest to smallest.

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• First I had to correct your link: it has a terminating “)” which makes it unfindable.

The 6 lengths and masses are, in order shown,

L M

2 2

1 2

2 1

3 1

2 4

1 1

A. Fundamental wavelength λ is proportional to L; λ = 2L. The L values are given, so you can figure out those rankings.

B. Wave speed v is proportional to sqrt(T); v = sqrt(T/(m/L)), where, in this case, m/L (the wire “linear density”) is constant. Tension T is just Mg, the M values are given, so you can figure out those rankings too.

If anyone were interested in ranking the frequencies, which is more interesting, f = v/λ and thus is proportional to sqrt(T)/L, or in this case sqrt(M)/L. The configurations 1 through 6 would be have relative frequencies 0.7, 1.4, 0.5, 0.33, 1.0, 1.0, and thus the rankings would be, lowest to highest frequency configuration numbers, 4, 3, 1, 5&6, 2.

• Brooke your problem seems to be you don’t know how to interpret algebraic expressions. That F = mg means, the force of gravity can be found by multiplying some mass m by the acceleration g due to gravity. So for… a) The force of gravity is found how? I just wrote it out above. And what I wrote can be succinctly and more precisely written as F = mg, the equation you gave us. Think about it. b) This is the same equation, F = mg, but the factors are rearranged so mass m is on the LHS of the = instead of force F. That is m = F/g. Were you required to have taken algebra before taking physics? If not, that’s your problem and that will haunt you throughout the physics course. And if that is the case, shame on your school for not preparing you for physics properly.

• the frequency from largest to smallest is B,EF,A,C,D