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Problem One. An aluminum wire of length 30.0 m is connected end-to-end with a copper wire of length of 20.0 m. Both have 1.00-mm diameters and are stretched to a tension of 140 N. 1.) Find how long (in seconds) it takes a transverse wave to travel the entire length of the two wires. The density of aluminum and copper are 2,710 kg/m³ and 8,920 kg/m³, respectively. (A) 0.769 (B) 0.637 (C) 0.367 (D) 0.118 (E) 0.258 2.) Consider if periodic wave pulses are sent down the wire with a frequency of 50.0 Hz by repeatedly plucking the wire a vertical distance of 3.00 cm. Write an expression for the traveling wave that is reflected off the boundary between the aluminum wire and copper wire. (A) y = 0.868 cm sin[(1.22 m?¹)x + (314 rad/s)t] (B) y = 0.868 cm sin[(4.57 m?¹)x - (314 rad/s)t] (C) y = 0.868 cm sin[(1.22 m?¹)x + (256 rad/s)t] (D) y = 1.06 cm sin[(1.22 m?¹)x - (314 rad/s)t] (E) y = 1.06 cm sin[(1.22 m?¹)x - (256 rad/s)t] 3.) Consider if the wave transmitted into the copper wire then reflects off of a perfectly rigid boundary on the right side of the copper wire. Write a general expression for the standing wave that would result in the copper wire. (A) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)] (B) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)] (C) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)] (D) y = 4.26 cm [sin(1.22 m?¹)x] ? [cos((314 rad/s)t)] (E) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)] 4.) If the left end of the aluminum wire is held at 30.0°C, and the right end of the copper wire is held at 90.0°C, find the temperature (in °C) at the junction of the two wires when the energy flow reaches a steady state. The thermal conductivity values, in W/m?°C, are 238 and 397 for aluminum and copper, respectively. (A) 67.5 (B) 63.7 (C) 93.7 (D) 118 (E) 72.3 5.) Find the thermal resistance along the length of the entire wire in units of °C/W. (A) 0.327 (B) 0.548 (C) 0.976 (D) 0.176 (E) 0.738

          Problem One. An aluminum wire of length 30.0 m is
connected end-to-end with a copper wire of length of
20.0 m. Both have 1.00-mm diameters and are
stretched to a tension of 140 N.

1.) Find how long (in seconds) it takes a transverse wave to travel the entire length of the two wires. The
density of aluminum and copper are 2,710 kg/m³ and 8,920 kg/m³, respectively.
(A) 0.769
(B) 0.637
(C) 0.367
(D) 0.118
(E) 0.258

2.) Consider if periodic wave pulses are sent down the wire with a frequency of 50.0 Hz by repeatedly
plucking the wire a vertical distance of 3.00 cm. Write an expression for the traveling wave that is
reflected off the boundary between the aluminum wire and copper wire.
(A) y = 0.868 cm sin[(1.22 m?¹)x + (314 rad/s)t]
(B) y = 0.868 cm sin[(4.57 m?¹)x - (314 rad/s)t]
(C) y = 0.868 cm sin[(1.22 m?¹)x + (256 rad/s)t]
(D) y = 1.06 cm sin[(1.22 m?¹)x - (314 rad/s)t]
(E) y = 1.06 cm sin[(1.22 m?¹)x - (256 rad/s)t]

3.) Consider if the wave transmitted into the copper wire then reflects off of a perfectly rigid boundary on
the right side of the copper wire. Write a general expression for the standing wave that would result in
the copper wire.
(A) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)]
(B) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)]
(C) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)]
(D) y = 4.26 cm [sin(1.22 m?¹)x] ? [cos((314 rad/s)t)]
(E) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)]

4.) If the left end of the aluminum wire is held at 30.0°C, and the right end of the copper wire is held at
90.0°C, find the temperature (in °C) at the junction of the two wires when the energy flow reaches a
steady state. The thermal conductivity values, in W/m?°C, are 238 and 397 for aluminum and copper,
respectively.
(A) 67.5
(B) 63.7
(C) 93.7
(D) 118
(E) 72.3

5.) Find the thermal resistance along the length of the entire wire in units of °C/W.
(A) 0.327
(B) 0.548
(C) 0.976
(D) 0.176
(E) 0.738

Problem One. An aluminum wire of length 30.0 m is
connected end-to-end with a copper wire of length of
20.0 m. Both have 1.00-mm diameters and are
stretched to a tension of 140 N.

1.) Find how long (in seconds) it takes a transverse wave to travel the entire length of the two wires. The
density of aluminum and copper are 2,710 kg/m³ and 8,920 kg/m³, respectively.
(A) 0.769
(B) 0.637
(C) 0.367
(D) 0.118
(E) 0.258

2.) Consider if periodic wave pulses are sent down the wire with a frequency of 50.0 Hz by repeatedly
plucking the wire a vertical distance of 3.00 cm. Write an expression for the traveling wave that is
reflected off the boundary between the aluminum wire and copper wire.
(A) y = 0.868 cm sin[(1.22 m?¹)x + (314 rad/s)t]
(B) y = 0.868 cm sin[(4.57 m?¹)x - (314 rad/s)t]
(C) y = 0.868 cm sin[(1.22 m?¹)x + (256 rad/s)t]
(D) y = 1.06 cm sin[(1.22 m?¹)x - (314 rad/s)t]
(E) y = 1.06 cm sin[(1.22 m?¹)x - (256 rad/s)t]

3.) Consider if the wave transmitted into the copper wire then reflects off of a perfectly rigid boundary on
the right side of the copper wire. Write a general expression for the standing wave that would result in
the copper wire.
(A) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)]
(B) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((314 rad/s)t)]
(C) y = 4.26 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)]
(D) y = 4.26 cm [sin(1.22 m?¹)x] ? [cos((314 rad/s)t)]
(E) y = 6.00 cm [sin(2.22 m?¹)x] ? [cos((256 rad/s)t)]

4.) If the left end of the aluminum wire is held at 30.0°C, and the right end of the copper wire is held at
90.0°C, find the temperature (in °C) at the junction of the two wires when the energy flow reaches a
steady state. The thermal conductivity values, in W/m?°C, are 238 and 397 for aluminum and copper,
respectively.
(A) 67.5
(B) 63.7
(C) 93.7
(D) 118
(E) 72.3

5.) Find the thermal resistance along the length of the entire wire in units of °C/W.
(A) 0.327
(B) 0.548
(C) 0.976
(D) 0.176
(E) 0.738

Added by Juan S.

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