exam_1_review

# Exam 1 review

This was given as a midterm (Exam 1) in 2014 by Prof. Kuzma.

## Front page

 2014 Physics 203 T-10 Exam 1 - Midterm Name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

### Instructions

• Please put away everything except:
1. this exam and your Scantron form (use back sides of these pages for drafts you don’t want to be graded).
2. one double-sided sheet of notes (formulas, etc.) that you prepared for this exam
3. calculator (must have no connection to internet and no text/picture storage)
4. pen/pencil/eraser
5. clock/watch (no connection to internet, no memory functions)
• Please make sure you are not sitting next to someone else, unless there is no such seats available.
• No exchange of information between students is allowed during the exam!
• Please do not open this booklet until you are instructed to do so. Please do not unstaple this booklet!
• Out of 4 problems, please cross one out, and attempt the other 3. For full credit, show your work!
• If you need to take a quick bathroom break:
• please leave this booklet with one of the proctors on your way out
• pick it up on your way back in.
• If you have a question:
• If you think some information is missing, please walk down to a proctor with your question.

### Select constants

• $p_A = 101.3 \times 10^3$ Pa
• $g = 9.8\,\frac{\text m}{{\text s}^2}$
• $N_A = 6.02 \times 10^{23}\,{\text{mol}}^{-1}$
• speed of sound $v$:
• $v_{\text{air}} = 343$ m/s
• $v_{\text{water}} = 1482$ m/s
• speed of light $c$:
• $c_{\text{vacuum}} = 3 \times 10^8$ m/s
• $\epsilon_0 = 8.85 \times 10^{-12}$ F/m
• $\mu_0 = 4\pi \times 10^{-7}\,\frac{\text N}{{\text A}^2}$

### SI prefixes ### Points summary

Part of the exam Score …out of maximum
Question 1 2.5
Question 2 2.5
Question 3 2.5
Question 4 2.5
Question 5 2.5
Question 6 2.5
Question 7 2.5
Question 8 2.5
Question 9 2.5
Question 10 2.5
Problem 1 25
Problem 2 25
Problem 3 25
Problem 4 25
Total: 100

## Questions

Professor, I had a quick question regarding practice exams…will you be posting keys for them or are we supposed to just use the wiki to ask if the answers we got are correct? I'm mostly asking since we did not have time to finish all the long form questions during lecture. -Nichole

• Answer: the key is posted on D2L under “Practice exams”

### Question 1

Which statement below IS NOT a property of a simple-harmonic oscillator?

• [….] A) The displacement from equilibrium can be represented by a general form $x = A \cos(2\pi f t + \theta_0)$
• [….] B) The maximum kinetic energy during an oscillation is equal to the maximum potential energy
• [….] C) The kinetic energy is zero when the system's displacement from the equilibrium point is maximal
• [….] D) The kinetic energy is maximal when the system's displacement from the equilibrium point is zero
• [….] E) The acceleration is zero when the system's displacement from the equilibrium point is maximal

### Question 2

As an electromagnetic wave propagates in vacuum, at some point in space and time, its $E$ field is pointing along the $+x$ axis in a right-handed coordinate system, and its $B$ field is pointing along the $+y$ axis. In which direction does this wave propagate? • [….] A) $+ z$ (out of the page)
• [….] B) $+ y$ (up)
• [….] C) $+ x$ (to the right)
• [….] D) $- y$ (down)
• [….] E) $- z$ (into the page)

### Question 3

A simple pendulum is a point mass $m$ suspended on a weightless string of length $l$. Which of the following will shorten the period of this pendulum?

• [….] A) Doubling of the mass $m$
• [….] B) Reducing the length $l$ by 10%
• [….] C) Increasing the amplitude of oscillations by giving the mass m an extra push
• [….] D) Placing the same system on the Moon
• [….] E) Increasing the length $l$ by 20%

### Question 4

A 1-kg mass is attached to a spring, and completes an oscillation cycle in 3.14 s. What is the spring constant?

• [….] A) 4 N/m
• [….] B) 0.25 N/m
• [….] C) 0.1 N/m
• [….] D) 10 N/m
• [….] E) 389 N/m

### Question 5

A zip-line spanning 200 m over a ravine consists of a 100-kg steel cable anchored between two trees at a tension of 20 kN. If one hops onto the zip-line near one end, how long would it take for a jolt to propagate all the way to the other end and back to the original point?

• [….] A) 1.2 s
• [….] B) 1 s
• [….] C) 28 s
• [….] D) 2 s
• [….] E) 8,000 s

### Question 6

On a nice summer evening (Portland style), a lightning is followed by thunder 10 s later. How far away is the lightning strike?

• [….] A) $34.4$ m
• [….] B) $343$ m
• [….] C) $3.43$ km
• [….] D) $3 \times 10^9$ m
• [….] E) $3 \times 10^7$ m

### Question 7

A resonant cavity in a whistle is exactly 3.43 cm long, featuring a closed end and an open end. Find the fundamental frequency.

• [….] A) 10 kHz
• [….] B) 117 kHz
• [….] C) 2.5 kHz
• [….] D) 5 kHz
• [….] E) 25 kHz

### Question 8

Screaming at a frequency of 1200 Hz as he is about to land, a young skydiver is descending at a speed of 2 m/s. What is the frequency of his own echo that he hears?

• [….] A) 1186 Hz
• [….] B) 1193 Hz
• [….] C) 600 Hz
• [….] D) 1207 Hz
• [….] E) 1214 Hz

### Question 9

What is the correct statement referring to a source of sound (such as a jet aircraft) traveling faster than the speed of sound?

• [….] A) A macroscopic object such as an aircraft cannot travel faster than the speed of sound in air
• [….] B) An object traveling faster than the speed of sound will absorb all of its emitted sound and implode
• [….] C) The emitted sound cannot propagate in front of the object
• [….] D) A sonic boom (the shock wave from the aircraft) is always heard before the aircraft can be seen
• [….] E) The wings of such an aircraft must be perpendicular to its body to minimize the drag force

### Question 10

What wave phenomena can be characterized by a 2 MHz frequency?

• [….] A) UV light and audible sound
• [….] B) X-rays and waves on a piano string
• [….] C) visible light and ocean waves
• [….] D) radio waves and ultrasound
• [….] E) gamma-rays and action potentials in neurons

## Problems

### Problem 1

The B string (medium gauge) on an acoustic guitar is made of 0.017-inch diameter stainless steel wire. It is usually tuned to 246.942 Hz, the B note almost an octave below the “middle A” (440 Hz). (unit conversion: 1 inch = 2.54 cm = 0.0254 m). Approximating the string as a cylinder of length $L = 65$ cm (between the bridge and the nut) and cross-sectional area $A = \pi r^2$ (where $r$ is the radius), and assuming the density of stainless steel $\rho = 8000\,{\text{kg}}/{\text m}^3$, find the following:

• A) [3 points] Convert the string diameter and length to SI units, and find the string radius and volume.
• B) [3 points] Find the string mass m and the linear mass density (mass per length) $\mu$. Indicate units!
• C) [4 points] Noting that the string is immobilized at both ends (at the bridge and at the nut), find the vibrational wavelength $\lambda_1$ of the fundamental harmonic of the string.
• D) [3 points] Using your answer in part C) and the 246.942 Hz value of the B-note frequency, find the velocity of propagation of the waves along the string, assuming the fundamental harmonic of the string is tuned to the B note.
• E) [4 points] Find the force of tension in the string necessary to tune its fundamental to the B note. Please specify both the value and the units.
• F) [3 points] What would be the fundamental frequency if the tension were reduced by 10% (that is, if the reduced tension were 0.90 times the tension found in part E)?
• G) [5 points] How far from the bridge (the bottom end of the string) the player has to press the string against the fretboard, in order for the new fundamental to produce the A sound (440 Hz)? Assume the tension in the string is still equal to that found in part E) when it is pressed against a fret. Hint: Only the bottom part of the string is plucked to make the sound. Assume the finger immobilizes the point of the string where it presses against a fret.

### Problem 2

A speedboat equipped with an underwater sound recording system is launched from the patrol ship at time $t = 0$. The diesel engine on the ship is producing under-water sound waves at a frequency 40.000 Hz. Both the boat and the ship are traveling in the same direction relative to the water, at $u_b =18$ m/s (35 knots) and $u_s = 5.15$ m/s (10 knots). (Hint: use the speed of sound in water on the front page of this exam)

• A) [3 points] Find the frequency of the sound waves that the speedboat would detect if it were to stop
• I am having a hard time understanding why we are using the minus sign while solving this doppler effect equation. It seems as though the frequency should decrease since the ship is traveling faster than the stopped speed boat. Aren't the two getting further apart?Angelique Vasquez 2015/04/18 13:08
• Good question! I think what is a bit unclear from the problem statement, is that the boat stops after some time after being launched. So it is essentially stopped in front of the ship, and the ship is moving towards the boat. If a similar misunderstanding happens in class during your exam, please ask to clarify.Prof. Nicholas Kuzma 2015/04/19 12:20
• B) [3 points] Find the frequency of the sound waves that the speedboat is detecting while it's moving
• Question: Is this the frequency of the sound waves while the speedboat is detecting while both the speedboat and the ship are moving? Or is it just the frequency while the speedboat is moving and the ship has stopped?Elin Odegard 2015/04/20 19:39
• Answer: in this part, both vessels are moving in the same direction, the boat is ahead of the ship
Prof. Nicholas Kuzma 2015/04/21 00:48
• C) [3 points] Find the wavelength of the sound waves in the water
• D) [1 point] Find the distance between the speedboat and the ship 1 minute after the boat is launched
• E) [3 points] How many wavelengths fit into the distance between the vessels found in part D)?
• F) [4 points] How many periods of the sound wave were emitted by the ship's engine in one minute?
• G) [4 points] How many periods of the sound wave were received by the moving speedboat in 1 min?
• H) [4 points] Explain the discrepancy between the answers in parts F) and G). Does part E) play any role?

### Problem 3

The electric field of an electromagnetic wave is defined by a set of equations: $E_x = 0$, $E_y =900\cdot\cos\big( 1.142\times 10^7\!\cdot x$ $-\;3.425\times 10^{15}\!\cdot t\big)$, $E_z = 0$, where all the numerical parameters are in SI units: $900$ V/m, $1.142\times 10^7$ m$^{-1}$, and $-3.425\times 10^{15}$ s$^{-1}$. Also, $x$ is the $x$-coordinate in meters and $t$ is the time in seconds. Referring to these equations and to the plots of $E_y(x)$ and $E_y(t)$ on the next page, find the following: • A) [3 points] What is the wavelength of this wave?
• B) [3 points] What is the period of this wave?
• C) [4 points] Knowing that the speed of light in a dense material is substantially slower than the speed of light in vacuum, can you tell if this wave is propagating in a dense material or in vacuum?
• D) [3 points] Find the direction in which this wave is propagating
• E) [4 points] Find the maximum magnetic field (magnitude and direction) of this wave.
• F) [4 points] Sketch the plot of the non-zero magnetic field component as a function of $x$ at $t = 0$. Please label the vertical axis (quantity plotted, units, and numerical values). • G) [4 points] Find the average intensity (time-averaged power per unit area) of this wave.

#### Plots for Problem 3

• Dependence of $E_y$ on the $x$ coordinate at time $t = 0$.
Note, the bottom scale is in units of $1 \mu$m = $10^{-6}$ m. • Dependence of $E_y$ on time $t$ at $x = 0$.
Note, the bottom scale is in units of 1 fs = $10^{-15}$ s. ### Problem 4

A simple pendulum consists of a mass $m = 0.1$ kg suspended on a string of length $L$ and has a period of 1 s.

• A) [4 points] What is the frequency of this pendulum? What is the angular frequency ω of the oscillations?
• B) [4 points] What is the length of this pendulum?
• C) [5 points] The pendulum is launched from rest by striking the mass with an impact that gives it an initial velocity $v_0 = 0.2$ m/s while it is still located at the equilibrium point. What is the maximum kinetic energy of the pendulum (ignore friction)?
• D) [3 points] What is the maximum potential energy of the pendulum?
• E) [4 points] What is the maximum elevation (height, measured vertically) of the pendulum relative to the equilibrium point?
• F) [5 points] What is the maximum angle from vertical that the pendulum swings at during oscillations?

(Hint: draw a triangle formed by the pendulum at its maximum angle and the vertical) 