String Frequencies A copper block is suspended in air from a wire in Part 1 of t
ID: 2111715 • Letter: S
Question
String FrequenciesA copper block is suspended in air from a wire in Part 1 of the drawing. A container of mercury is then raised up around the block as in Part 2. The fundamental frequency of the wire is given by f1 = nv 2L , with n = 1, v is the speed at which individual waves travel on the wire and L is the length of the wire.
(a) How is the speed v related to the tension F in the wire? v is directly proportional to F . v is inversely proportional to F. v is directly proportional to F2 . v is inversely proportional to F . v is directly proportional to F.
(b) Is the tension in the wire in Part 2 of the drawing less than, greater than, or equal to the tension in Part 1? The tension in the wire in Part 2 is less than the tension in Part 1. The tension in the wire in Part 2 is greater than the tension in Part 1. The tension in the wire in Part 2 is equal to the tension in Part 1.
(c) Is the fundamental frequency of the wire in Part 2 of the drawing less than, greater than, or equal to the fundamental frequency in Part 1? The fundamental frequency of the wire in Part 2 is less than the fundamental frequency in Part 1. The fundamental frequency of the wire in Part 2 is greater than the fundamental frequency in Part 1. The fundamental frequency of the wire in Part 2 is equal to the fundamental frequency in Part 1.
In Part 2 of the drawing some (56.0%) of the block's volume is submerged in the mercury. The density of copper is 8890 kg/m3, and the density of mercury is 13 600 kg/m3.
(d) What is the algebraic expression that gives the fundamental frequency f1? Express your answer in terms of the tension F in the wire, the length L of the wire, and the mass m of the wire.
f1 =
(e) What is the algebraic expression that gives the tension FPart 1 in Part 1 of the drawing? Express your answer in terms of the density %u03C1copper of copper, the volume V of the block, and the magnitudeg of the acceleration due to gravity.
FPart 1 =
(f) What is the algebraic expression that gives the tension FPart 2 in Part 2 of the drawing? Express your answer in terms of the density %u03C1copper of copper, the volume V of the block, the density %u03C1mercuryof mercury, the volume Vsubmerged of the block that is submerged in the mercury, and the magnitudeg of the acceleration due to gravity.
FPart 2 =
(g) What is the ratio of the fundamental frequency f1, Part 2 of the wire in Part 2 to the fundamental frequency f1, Part 1 of the wire in Part 1 of the drawing?
f1,part 2 f1,part 1 =
Explanation / Answer
a)v=(T/u)
but T=F
so velocity is directly proportional to (F)^0.5
b)The tension in the wire in Part 2 is less than the tension in Part 1.
since an upward buyant force is acting on the block
c)The fundamental frequency of the wire in Part 2 is less than the fundamental frequency in Part 1.
since F2 is less than F1
d)v=(F/u)^0.5
=(F*L/m)^0.5
e)tension F=mg
but m=volume*density
=v*rho*g
f)F=mg-ph *g*v
=vg*(pcu -pgh)
but since pcu <phg
so tension F=0
g)ratio=0
since F2=0