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Physics 123 A&B, Winter 2014 Midterm Exam 1, page 1

Part I. [43 Points] Please be sure to mark all answers for problems 1-12 on your scantron sheet!!

1. [5 points] If one could transport a simple pendulum of constant length from the Earths surface to the Moons, where the acceleration due to gravity is one-sixth (1/6) that of the Earth, by what factor would the pendulum frequency be changed?

A. 0.17 B. 0.41 C. 1.0 (no change) D. 2.5 E. 6.0

For questions 2-5 consider the below ball moving with simple harmonic motion between positions 1 and 4.

-0.3 m -0.2 m -0.1 m 0.0 m 0.1 m 0.2 m 0.3 m

Position1

Position2

Position3

Position4

2. [5 points] What is the position closest to where the ball reaches its maximum speed?

A. -0.3 m only B. +0.3 m only C. -0.3 and +0.3 m D. 0.0 m E. +0.2 m

3. [5 points] What is the position closest to that of maximum acceleration?

A. -0.3 m only B. +0.3 m only C. -0.3 and +0.3 m D. 0.0 m E. +0.2 m

4. [5 points] If the magnitude of the acceleration at position 1 is 3.0 /2, what is the frequency?

A. 0.1 Hz B. 0.3 Hz C. 0.5 Hz D. 1.6 Hz E. 3.2 Hz

5. [5 points] You alter the system so that when you release the ball from position 1 at time t = 0 s, it arrives for the first time at position 3 at t = 0.4 s. What is the magnitude acceleration at position 3?

A. 0.88 /2 B. 1.4 /2 C. 3.1 /2 D. 6.6 /2 E. Cant be determined

Name ______________________________________Student ID __________________ Score___________

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Physics 123 A&B, Winter 2014 Midterm Exam 1, page 2

A loudspeaker at a rock concert generates 102/2 at 19.0 m at a frequency of 1.0 kHz. Assume the speaker spreads its energy uniformly in three dimensions.

6. [5 points] What is the total acoustic power output of the speaker?

A. 0.055 B. 0.13 C. 2.4 D. 22 E. 45

7. [5 points] At what distance will the intensity be at the pain threshold of 1.0 /2?

A. 0.06 m B. 0.10 m C. 1.9 m D. 3.6 m E. 19 m

8. [5 points] What is the intensity at 50.0 ?

A. 0.00051 /2 B. 0.0014 /2 C. 0.01 /2 D. 0.17/2 E. 0.1 /2

9. [3 points] Two waves are propagating along a string: 1(, ) = 1sin ( ) and 2 = 2cos ( + ). Which value of will make for total constructive interference?

A. 0

B. /4 C. /2 D. E. They are traveling in opposite directions, so there will never be constructive interference.

Name __________KEY________________________ Student ID _______________ Score_______

last first Lab Question (12 Points)

A setup for a vibrating string experiment allows for varying both the tension (weight) and the string length. The distance between the pulley and the end of the vibrator is 100 cm With the Vibrator frequency set at 180 Hz, three antinodes are observed 10 [4 points] What is the fundamental frequency of this setup?

(a) 60 Hz (b) 120 Hz (c) 180 Hz (d) 240 Hz (e) 360 Hz

11 [4 points] What is the wave speed

(a) 30 m/s (b) 60 m/s (c) 120 m/s (d) 165 m/s (e) 600 m/s

12 [4 points] Now the string length or tension is varied (not both at the same time) enough to increase

or decrease the number of antinodes by one. Which of the circled answers below is incorrect?

(a) A (b) B (c) C (d) D (e) E

String length

Increased

String length

Decreased

Tension

Increased

Tension

Decreased

Number of

antinodes Decreases Increases Decreases Increases

Wavelength Same Same Increases Decreases

Fundamental

frequency Decreases Increases Increases Decreases

Fundamental

wavelength Increases Decreases Same Same

Wave speed Same Same Increases Decreases

Vibrator

Weight

(A)

(B)

(C)

(D)

(E)

(B)

(F)

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Physics 123 A&B, Winter 2014 Midterm Exam 1, page 1

PartII. [25 Points] Please write down all derivation steps in detail in order to get full points!! An object of mass m is suspended from a vertical spring with spring constant 1692 N/m.

When the object is pulled down 2.47 cm from its equilibrium position and released from rest,

the object oscillates at 5.30 Hz.

1. (3 points) Find m.

2p f =w =k

mm =

k

(2p f )2=

1692N /m

(2p5.3s-1)2=1.53kg

2. (9 points) Write expressions for the displacement, the velocity, and the acceleration as functions of time t: x(t), v(t), a(t). Show units where needed. Show how you found all the constants.

x(t)=2.47 cos(wt +d) cm,

w = 2p f = 33.3rad / s-1

Initial condition gives x(0)=-2.47cm = 2.47 cos(d)cm d = p x(t)=2.47 cos(33.3 t + 3.14) cm

v(t)=dx/dt = -82.3 sin(33.3 t + 3.14) cm/s

a(t)=dv/dt = - 2741 cos(33.3 t + 3.14) cm/s-2

Two speakers are separated by 4.5 m as shown. An observer at point O, 6.0 m directly in front of speaker 1

at point A, hears the loudest sound (completely constructive interference) when both speakers are driven in

phase at a certain common frequency. Assume that the speed of sound in

air is 340 m/s.

3. (5 pts) What is the largest wavelength for which the observer would experience completely constructive interference?

The constructive interference satisfies condition d = 2pDx / l The maximum wavelength is when d = 2plmax =Dx

SinceDx = OB - OA = 7.5-6.0 =1.5m. Tha maximum wavelength is 1.5m

4. The frequencies of speaker 1 and speaker 2 are tuned to 684 Hz and 680 Hz, respectively. 4.a (3 pts) What is the beat frequency heard by the observer?

beat frequency = 684Hz-680Hz=4Hz

4.b (5 pts) The speaker 1 is moved away from the observer along OA direction with constant speed us. The observer receives the same frequency from both speakers. What is the value of us?

fr =vfs

v+us us =

vfs

fr- v =

340 684

680-340 = 2m / s

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Physics 123A, Winter 2014 Exam 1 WO-UWA123A141T-E1(SPR)Sol.doc

III. [20 points total] This question consists of two unrelated parts, A and B. A. Students 1 and 2 each generated a single transverse pulse by moving the ends of a spring back and

forth once at unknown times. Each pulse was generated on a single side of the spring. Originally, there was a line of cups along one side of the spring. Only two of the cups were disturbed, as shown. Ignore reflected pulses.

disturbed cupsStudent 1 Student 2

Top view

i. [5 pts] Were the pulses traveling on the same or the opposite sides of the spring? Explain.

Since some of the cups were knocked over, at least one of the pulses must have been on the bottom side of the spring. However, since most of the cups were undisturbed (and the undisturbed cups are found on both sides of the location of the disturbed cups), the amplitude of the pulse must have been smaller than the distance between the equilibrium position of the spring and the cups. Therefore, for any of the cups to be knocked over, the second pulse must also have been generated on the bottom side of the spring; the two pulses must have interfered constructively to knock over the cups.

ii. [5 pts] Was the propagation speed of the pulse generated by student 1 greater than, less than, or equal to the propagation speed of the pulse generated by student 2? If there is not enough information provided, state so explicitly. In either case, explain. From the tutorial Superposition & reflection of pulses, the propagation speed of pulses is determined by the medium. Since both pulses travel on the same medium, the propagation speeds of the two pulses were the same.

B. A pulse moves toward the right end of a spring. The top-

view diagram at right shows the shape of the spring just before the pulse reaches the boundary. A cup has been placed near the right end of the spring as shown. i. [5 pts] Suppose the end of the spring were fixed in

place. During the time interval in which the pulse reflects from the fixed end, will the cup be disturbed? Explain. We can think of the pulse as being composed of a front pulse (on the bottom of the spring) and a rear pulse (on the top of the spring). The front pulse will be reflected on the opposite side of the spring (i.e., the top) since the end of the spring is fixed. The peak of this reflected front pulse will superpose with the peak of the incident rear pulse near the cup, yielding a transverse displacement of 3 units toward the top of the page, which will disturb the cup.

ii. [5 pts] Suppose the end of the spring were free to move along a rod. During the time interval in which the pulse reflects from the free end, will the cup be disturbed? Explain. The front pulse would be reflected on the same side (i.e., the bottom side) of the spring since the end of the spring is free. Since the superposition of the reflected front pulse and the incident rear pulse would yield a transverse displacement of 1 unit toward the bottom of the page, the cup would not be disturbed.

cup fixed orfree