I.  You are holding a 1.6 m solid brass rod by a movable clamp that is located in the middle of the rod. You then strike the rod so that it resonates.

a)  Draw the resulting standing wave pattern below.

b)  The frequency heard is 1000 Hz. Describe how you could change this experiment to hear a frequency of 2000 Hz.

c)  Determine the speed of sound in brass.

II.  At the surface of the sun the temperature is about 6000 K and all the substances present are gaseous.

a)  Calculate the root mean square speed and the internal energy of 2 moles of helium gas at the sun's surface. (MHe=4 g/mol)

vrms=

UHe=

b)  At the surface of the sun, two moles of helium gas undergo an isothermal process during which the pressure doubles. Sketch this process on the P-V diagram below and label the final state.

c)  Determine Vf in terms of Vi only.

Vf =

3.  A jet engine emits a whine of frequency 3000 Hz. When the engine is moving directly away from an observer at half the speed of sound, an observer hears a frequency of

a)  1000 Hz

b)  1500 Hz

c)  2000 Hz

d)  4500 Hz

e)  6000 Hz

  1. A string whose length is 4 m is fixed at both ends and vibrates according to the equation

y(x, t) = 0.04 sin px cos 2pt

where the units are SI. The total number of nodes exhibited by the string is

a)  1

b)  2

c)  3

d)  4

e)  5

5.  An ideal gas whose original temperature and volume are 27ºC and 0.283 m3 undergoes an isobaric expansion. If the final temperature is 87ºC, then the final volume is approximately

a)  0.0340 m3

b)  0.0552 m3

c)  0.170 m3

d)  0.340 m3

e)  1.45 m3

6.  A 6.0-g lead bullet traveling at 300 m/s penetrates a wooden block and stops. If 50 percent of the initial kinetic energy of the bullet is converted into thermal energy in the bullet, by how much does the bullet's temperature increase? (The specific heat of lead is 128 J/kg · K.)

a)  0.17 Cº

b)  1.8 x 102 Cº

c)  17 Cº

d)  3.5 x 102 Cº

e)  35 Cº

7.  The heat capacities of both ice and steam are 2.09 kJ/kg · Cº and the latent heats of fusion and vaporization of water are Lf= 333.5 kJ/kg and Lf= 2257 kJ/kg . The quantity of heat required to change 1.00 kg of ice at –10.0ºC to steam at 120ºC is approximately

a)  3130 kJ

b)  3070 kJ

c)  2630 kJ

d)  2590 kJ

e)  2320 kJ

8.  An ideal gas initially at 50ºC and pressure P1 = 100 kPa occupies a volume V1 = 3 x 10-3 m3. It undergoes a quasi-static, isothermal expansion until its pressure is reduced to 50 kPa. How much heat enters the gas during this process? R = 8.314 J/mol·K

a)  116 J
b)  208 J
c)  256 J
d)  304 J
e)  416 J /