p250 Fa23 Exam 1 vA (1)

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University of Michigan *

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Physics

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Feb 20, 2024

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First Name: Last Name: UMID: Physics/BioPhysics 250 Fall 2023 - Exam #1 Form 1 READ THIS BEFORE YOU BEGIN  Print your name and UMID in the boxes provided above (please write neatly so the scanner can pick it up).  Fill in your name , UMID number , and form number (under “key”) on your scantron sheet  This is a one hour and 50 minute, closed book exam.  You may use a calculator; please do not share calculators.  The exam includes 20 multiple choice questions which will be machine graded. Each question is worth 5 points. No partial credit will be given.  You may use one 8.5×11” sheet of paper with hand-written notes written on both sides.  If you are stuck on a problem, move on and come back to it. Constants you might need 𝑘𝑘 = 8.99 × 10 9 N m 2 /C 2 𝜀𝜀 0 = 8.85 × 10 − 12 C 2 /N m 2 𝑔 = 9.8 m/s 2 Speed of sound in air at 20C = 340m/s Density of air at 20 C = 1.20 kg/m 3 Magnitude of the electron charge: 𝑒 = 1.6 × 10 −19 C Mass of the proton: 𝑚 𝑝 = 1.67 × 10 −27 kg Mass of the electron: 𝑚 𝑒 = 9.11 × 10 −31 kg 1 electron volt (1eV) = 1.6 × 10 −19 J Avogadro’s Number: 𝑁 𝐴 = 6.02 × 10 23 /mol Threshold of hearing 𝐼 𝑜 = 10 −12 W/m 2 milli(m) = 10 −3 , micro( 𝜇 ) = 10 −6 , nano (n) = 10 −9 pico (p) = 10 −12 , femto(f) = 10 −15 kilo (k) = 10 3 , mega (M) = 10 6 , giga (G) = 10 9

Passage for questions 1-3: The Stethoscope A stethoscope is a medical device for listening to sounds inside the human body. It commonly consists of a chest piece that is connected to PVC tubing, which then splits into two shorter metal tubes that direct the sound to the ears of the physician. The chest piece often has two sides: an open “bell” to better hear low-frequency sounds, and a similarly shaped hollow cavity that is covered with a flexible membrane, the diaphragm, for higher-pitched sounds. Use 𝑣 = 340 𝑚⁄𝑠 for the speed of sound and 𝜌 = 1.2 𝑘𝑔⁄𝑚 3 for the density of air for the problems below. 1. If the bell has a diameter of 25 mm on the open side that is pointing towards the patient, and the two eartips have circular openings with a diameter of 2.5 mm, by how much has the total sound intensity that reaches the physician’s ears increased, compared to what entered the bell? Assume that there are no losses in the tubing. A. It did not increase. B. By a factor of 5 C. By a factor of 10 D. By a factor of 50 E. By a factor of 1000

2. It is sometimes asserted that the bell is particularly good at amplifying low-frequency sounds below 100Hz because those sounds can excite standing waves in the air inside the bell, with one end open (towards the patient) and the other end almost closed. Do you believe this, based on what you know about the physics of standing waves and the basic geometry of the stethoscope? A. Yes, this is plausible. B. No, the bell is too small to accommodate standing waves at these frequencies. C. No, the bell is too large to accommodate standing waves at these frequencies. D. No, because standing waves need closed ends on both sides in order to form. E. No, because the open end becomes a closed and when pressed against the patient’s chest, and no sound will enter the bell. 3. A physician can hear sounds at a frequency of 100 Hz if the sound at the diaphragm has an intensity of at least 10 -10 W/m 2 . What is the displacement amplitude at the diaphragm for this sound? A. 15 pm B. 1.1 nm C. 11 µm D. 0.3 mm E. 12 mm END OF PASSAGE QUESTIONS

4. Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I. 𝑦 = 0.12 cos(−1.5𝑥 + 2𝑡) II. 𝑦 = −0.12 cos(2𝑥 + 1.5𝑡) III. 𝑦 = −0.02 cos(3𝑥 − 4𝑡) IV. 𝑦 = 0.02 cos(−2𝑥 + 2.5𝑡) Which of these waves have the same speed? A. I and II B. I and III C. I and IV D. II and III E. III and IV 5. A phon is an experimentally derived unit of human-perceived loudness. A person perceives sound at 800 Hz to be 40 phons, which corresponds to an intensity level of 40dB (from the graph). The person hears a different sound at 100 Hz to also be 40 phons, which corresponds to 60 dB. Approximately what is the ratio of the intensity of the 800 Hz sound to the 100 Hz sound, i.e. what is 𝐼 800𝐻𝑧 /𝐼 100𝐻𝑧 ? A. 100 B. 0.050 C. 0.01 D. 20 E. 0.10 Intensity level (dB)

6. Two speakers are set up and connected to the same 1000 Hz signal source. When you stand at a particular location between the two speakers you find that the two speakers individually produce a wave with amplitude 𝐴 . When both speakers are powered, you expect: A. An amplitude which goes from 0 to 𝐴 , as the phase difference of the sound coming from the two speakers changes from 0 to 2𝜋 radians. B. An amplitude of 𝐴 when the phase difference of the sound coming from the two speakers at your position is 0. C. An amplitude of 4𝐴 when the phase difference of the sound coming from the two speakers at your position is 0 radians. D. An amplitude which goes from 0 to 2𝐴 as the phase difference of the sound coming from the two speakers changes from 𝜋 to 2𝜋 radians. E. The phase difference of the sound coming from the two speakers at your position is always zero. 7. A guitar string plays a “G” note with a frequency of 196Hz when it is tuned to a tension of 70.0 N. A guitarist wishes to “bend” the note to a G# with a frequency of 207.65Hz. This is done by changing the tension in the string without appreciably changing its length. What string tension is required to play a G#? A. 72.1 N B. 68.0 N C. 66.1 N D. 74.2 N E. 78.6 N

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