Physics Lecture Review for Final Exam

1. Lecture 30 Goals: • Wrap up chapter 20. • Review for the final. • Final exam on Friday, Dec 23, at 10:05 am in BASCOM 272. Final will cover Chapters 1-20 (excluding Chapter 13). Semi-cumulative. • HW 12 due tomorrow night.

2. The Doppler effect • The frequency of the wave that is observed depends on the relative speed between the observer and the source. vs observer

3. The Doppler effect • Approaching source: f=f0/(1-vs/v) • Receding source: f=f0/(1+vs/v)

4. Waves • The figure shows a snapshot graph D(x, t = 2 s) taken at t = 2 s of a pulse traveling to the left along a string at a speed of 2.0 m/s. Draw the history graph D(x = −2 m, t) of the wave at the position x = −2 m.

5. History Graph: D(x = −2 m, t) 2 -2 3 4 6 7 2 5 time (sec)

6. A concert loudspeaker emits 35 W of sound power. A small microphone with an area of 1 cm2 is 50 m away from the speaker. • What is the sound intensity at the position of the microphone? • How much sound energy impinges on the microphone each second?

7. Psource=35 W R=50 m • The power hitting the microphone is: R Pmicrophone= I Amicrophone

8. Intensity of sounds • If we were asked to calculate the intensity level in decibels: I0: threshold of human hearing I0=10-12 W/m2

9. Suppose that we measure intensity of a sound wave at two places and found them to be different by 3 dB. By which factor, do the intensities differ?

10. Engines • For the engine shown below, find, Wout, QH and the thermal efficiency. Assume ideal monatomic gas. 4Pi Q=90J Pi Q=25J Vi 2Vi

11. First, use the ideal gas law to find temperatures 8Ti 4Ti 4Pi Q=90J 2Ti Pi Ti Q=25J 2Vi Vi • From the right branch, we have: nCVΔT=90 J n(3R/2)6Ti=90J nRTi=10J

12. Work output is the area enclosed by the curve: 8Ti 4Ti 4Pi Q=90J 2Ti Pi Ti Q=25J 2Vi Vi Wout=area=3PiVi=3nRTi=30J

13. From energy conservation: Wout=QH-QC Wout=30J QC=115J QH=145J • The thermal efficiency is: η=0.2

14. The Carnot Engine • Carnot showed that the thermal efficiency of a Carnot engine is: • All real engines are less efficient than the Carnot engine because they operate irreversibly due to the path and friction as they complete a cycle in a brief time period.

15. For which reservoir temperatures would you expect to construct a more efficient engine? A) Tcold=10o C, Thot=20o C B) Tcold=10o C, Thot=800o C C) Tcold=750o C, Thot=800o C

16. Kinetic theory • A monatomic gas is compressed isothermally to 1/8 of its original volume. • Do each of the following quantities change? If so, does the quantity increase or decrease, and by what factor? If not, why not? a. The temperature b. The rms speed vrms c. The mean free path d. The molar heat capacity CV

17. The average translational kinetic energy is: εavg=(1/2) mvrms2=(3/2) kBT • Mean free path is the average distance particle moves between collisions: N/V: particles per unit volume • The specific heat for a monatomic gas is: CV=3R/2 (monatomic gas)

18. Simple Harmonic Motion • A Hooke’s Law spring is on a horizontal frictionless surface is stretched 2.0 m from its equilibrium position. An object with mass m is initially attached to the spring however, at equilibrium position a lump of clay with mass 2m is dropped onto the object. The clay sticks. What is the new amplitude? 2m k m 2m k m -2 0(≡Xeq) 2

19. The speed when the mass reaches the equilibrium position: ½ k A2=½ m vmax2 vmax=ωA • The speed after clay sticks can be found using momentum conservation: m vmax=(m+2m)vnew vnew=vmax/3 • The new amplitude can be found using energy conservation: ½ (m+2m)vnew2=½ k Anew2 Anew=A/√3

20. (A)r1 < r2 (B)r1 = r2 (C)r1>r2 Fluids • What happens with two fluids? • Consider a U tube containing liquids of density r1 and r2 as shown: Compare the densities of the liquids: r2 r1

21. (A)r1 < r2 (B)r1 = r2 (C)r1 > r2 Fluids • What happens with two fluids?? • Consider a U tube containing liquids of density r1 and r2 as shown: • At the red arrow the pressure must be the same on either side. r1 x = r2 y • Compare the densities of the liquids: r2 y r1 x