Solutions to Homework #3 for Physics
104, Summer 2003
Exercises 29, 32, 15, 23
15. A blackbody is a perfect absorber of heat (epsilon = 1).
A blackened pan approximates this and thus, absorbs heat more than a shiny one.
23. In a 3-way bulb, any filament that is ON is at full temperature (yellow-white
light). Operating a 150-W bulb on only 50 W of current drives the filament at
less than full temperature, so the color shifts more to the 'cooler' side of the
29. Metal has a larger coefficient of thermal expansion compared to glass.
Thus, when heated under hot water for a moment, the metal expands more than
glass, thus loosening the grip between them.
32. The open refrigerator will tend to cool the air right in front of it
and dump heat at its back. Since the unit would deliver more heat to the
hotter air than it would absorb from the colder air, it would increase
the total amount of thermal energy in the room. On the average, the room would
then become warmer.
4. To find out the radiation from the foil, we need to know its temperature.
The dish is radiating with power P1 = 20 W and with emissivity e1=0.4. These
can be used to find the dish's temperature. Since the aluminum will be at
this temperature, and since aluminum has an emissivity e2=0.08, one
can then calculate the radiated power of the aluminum. One can solve this
also by ratio and proportion:
P1=sigma x e1 x A x T^4 while P2 = sigma x e2 x A x T^4.
Dividing one by the other equation, we get:
P1/P2 = (e1/e2) or substituing the values, we get P2= 4 W
Exercises 15, 20. 22. 23. 26
15. To raise the pitch (frequency), we can reduce the mass, shorten the
string or increase the tension.
20. The highest pitch strings are typically the thinnest, and therefore,
more prone to breakage.
22. Since the fundamental frequency in a wave is inversely proportional to the
square root of the medium's density, reducing the density by replacing
air by helium will increase the frequency.
23. The piccolo, being shorter than the flute, will have a higher pitch,
since the wavelengths are shorter.
26. The tuba, being longer than the trumpet, will have long wavelengths
for its fundamental frequency modes. This corresponds to lower frequency