Question

A combination work of art/musical instrument is illustrated. Four 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 or 2 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. Treat the strings as fixed at both ends; a good approximation due to the large inertial masses hanging from the end. (a) Rank the wave speeds in each wire, greatest first. (b) Rank the fundamental wavelength of wire, greatest first. (c) Rank the frequency produced by each wire, greatest first. Justify each ranking.

http://www.physics.oregonstate.edu/~walshke/COURSES/ph202/ph202_w14_rhw7.pdf

Answer 1

Answer 2

f = v/2L and v = sqrt(F/?) since the wires are identical ? is he same for each and F is the weight hanging which vary as the masses

so the frequencies will vary as (sqrt(m))/L

so in order presented we have

A) ( sqrt(2))/2 = 0.707

B) (sqrt(2))/1 = 1.414

C) (sqrt(1))/2 = 0.5

D) (sqrt(1))/3 = 0.333

E) (sqrt(4))/2 = 1.0

F) (sqrt(1))/1 = 1.0

So in order of highest to lowest

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

Answer 3

let wires be A(2,2) B(2,1) C( D E F9mass,length

1..With all the strings made of identical wire, wave speed u is proportional to ?T = ?(m*g), so the ranking would be the same as the number of masses hung on each wire: i.e (C,D,F), (A,B), E

2. fundamental wavelength of wire, ? = 2*(wire length)   (B,F), (A,C,E), D

3f = v/2L and v = sqrt(F/?) since the wires are identical ? is he same for each and F is the weight hanging which vary as the masses

so the frequencies will vary as (sqrt(m))/L

so in order presented we have

A) ( sqrt(2))/2 = 0.707

B) (sqrt(2))/1 = 1.414

C) (sqrt(1))/2 = 0.5

D) (sqrt(1))/3 = 0.333

E) (sqrt(4))/2 = 1.0

F) (sqrt(1))/1 = 1.0

So in order of highest to lowest

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