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AP1 Test Review D16 ­ 2016.notebook
A hollow tube of length L open at both ends as shown, is held in midair. A tuning fork with a frequency f o vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency. Express your answers to the questions below in terms of L and fo.
A) Determine the wavelength of the sound.
May 02, 2016
L
λ = 2L
B) Determine the speed of sound in the air inside the tube.
v = fλ = fo(2L)
C) Determine the next higher frequency at which this air column would resonate.
The next harmonic is the 2nd harmonic, which has
a frequency 2x the fundamental, so f = 2fo
The tube is submerged in a large, graduated cylinder filled with water. The tube is slowly raised out of the water and the same tuning fork, vibrating with frequency fo, is held a fixed distance from the top of the tube.
D) Determine the height h of the tube above the water when the air column resonates for the first time. Express your answer in terms of L.
h = ¼λ =¼(2L) = ½L
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AP1 Test Review D16 ­ 2016.notebook
May 02, 2016
In a physics lab, students will compare two circuits shown above. In one circuit, lightbulbs A and B will be connected to a battery in series. In the other circuit, lightbulbs C and D will be connected to an identical battery in parallel. All four lightbulbs are identical.
Student 1 predicts that the bulbs will be brighter in the series arrangement, while student 2 disagrees and predicts that the bulbs will be brighter in the parallel arrangement. Their arguments are as follows:
Student 1: “Bulbs A and B will be brighter than C and D because in the series circuit, each bulb gets all the current coming out of the battery. But in the parallel circuit each bulb gets only half the current.”
Student 2: "But you're not taking into account that bulb A uses up some of the current before it reaches bulb B, making the bulbs dimmer in the series circuit. And in the parallel circuit, the full voltage is across each bulb, so it's as if the other bulb weren't even there. So bulbs C and D will be brighter."
(a) i. Which aspects of Student 1’s reasoning, if any, are correct? Explain your answer.
Student 1's reasoning is correct that bulbs A and B will both get all of the current because there is only one "loop".
Student 1's reasoning is also correct that bulbs C and D will only get half the current because it will split evenly into the two pathways of equal resistance. ii. Which aspect of Student 1’s reasoning, if any, are incorrect? Explain your answer.
Student 1 is incorrect in assuming that getting the full current in the series circuit is necessarily more than half the current in a parallel circuit.
iii. Which aspect of Student 2’s reasoning, if any, are correct? Explain your answer.
Student 2 is correct in stating that both C and D will get the full voltage since they both are directly connected to the battery in the parallel circuit.
iv. Which aspect of Student 2’s reasoning, if any, are incorrect? Explain your answer.
Student 2 is incorrect in stating that A uses up some of the current. In a series circuit the current is the same in all parts of the circuit.
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AP1 Test Review D16 ­ 2016.notebook
May 02, 2016
Together the students write the following equations to describe the two circuits.
Series Arrangement
Parallel Arrangement
Equation 1: IS = IA = IB
Equation 3: IP = IC + ID
Equation 2: ΔV – IARA – IBRB = 0 Equation 4: ΔV – ICRC = ΔV – IDRD = 0
(b) i. Indicate all of the equations above that support Student 1’s reasoning, and explain how each equation provides support.
Equation 1 supports Student 1's reasoning that the current is equal throughout the series circuit for bulb A and B.
Equation 2 supports Student 1's reasoning that each bulb (C and D) gets half the current in the parallel circuit, because if you add them together you get the total current.
ii. Indicate all of the equations above that support Student 2’s reasoning, and explain how each equation provides support.
Equation 4 supports Student 2's reasoning that C and D get the total voltage. The voltage of the battery is ΔV and the voltage used on the resistors is ICRC and IDRD. (c) Resolve the two lines of reasoning about the two circuits to conclude which arrangement will have brighter bulbs. Use the equation above and any other equations that you need, and explain how the equations support your conclusion.
With all four bulbs being identical, the brightness will proportional to the current. To determine which gets more current from the same battery, the total resistance of each circuit must be determined. In the series circuit, the resistances are added together for a total current of 2R. In the parallel circuit, the resistance is the reciprocal of the sum of the reciprocals of each resistance, which gives a total resistance of 1/2 R. This means that the resistance of the parallel circuit is one‐fourth that of the series circuit which (using V = IR) means that it will get four times as much current. Using Equation 3, that will mean C and D will still get twice the total current in the series circuit, which according to Equation 1 is what each A and B get. Since C and D get more current, they will be brighter.
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