PHYS 201 TEST
#5 12/10/10 DR. HOLMES NAME
Do all five problems. All answers should be
in MKS units unless otherwise indicated. Show your work for partial credit.
1) A mass of 400 grams pulls down on a
spring which stretches 16 cm from its original uncompressed position
due to the weight.
a) What is the spring constant, k, of the
spring?
24.5 Nt/m
b) If this mass is stretched 2 cm
from the equilibrium position (which will be 18 cm from its equilibrium
position) and then released, it will oscillate. What will be the period, T, of
its oscillation?
0.803 sec
c) ) If the amplitude is increased 2 cm to 4 cm, that is, the
spring is stretched 4 cm from the equilibrium position and then released, will
the period of oscillation [increase, stay the same, or decrease]?
stay the same
d If a second identical spring is used in parallel with the first
spring so that the 400 gram mass stretches this “new” spring 8 cm (half the
original 16 cm) from its original position
(assume amplitude remains at 2 cm
and mass remains at 400 grams), will the period of oscillation [increase, stay
the same, or decrease]?
decrease
e) If the original spring is used (from
parts a&b), but the mass that is oscillating in decreased from 400 grams to
200 grams, assuming the amplitude remains at 2 cm, will the period of
oscillation [increase, stay the same, or decrease]?
decrease.
2) A certain piano string has a length of
0.57 meters and a mass density of 0.63 grams/meter. A tension of 24 Nt. is
applied to it.
a) What will be the speed of the wave on
this string?
195.18 m/s
b) What will be the fundamental frequency
when it is plucked?
171.2 Hz.
c) If a fundamental frequency of 262
cycles/sec (middle C note) is desired, what should the tension in the string
be?
56.2 Nt.
d) If a different string of the same length
but a smaller mass density is used, and if the original tension of 24 Nt is
applied, will the fundamental frequency for this string be [higher, the same,
or lower] than for the string in part (b)?
higher.
3) a) What is the speed of sound in air that
is at a temperature of 110oF ?
355.8 m/s = 797 mph.
b) What is the frequency of a 45 cm
wavelength sound wave in this air?
790.7 Hz
c) What is the wavelength of a 450 Hz sound
wave in this air?
0.791 m
d) If the temperature of this air were lowered
and the frequency of the sound wave were kept the same, would the wavelength of
the sound wave [increase, stay the same, or decrease] ?
decrease
e) If helium (molar mass of helium is 4
gm/mole, and helium is a monatomic gas, not a diatomic gas like N2
and O2) were used instead of air, and if the temperature and
wavelength of the sound were the same, would the frequency be [lower, the same,
or higher than] the frequency of this sound in air?
higher .
4) A source of sound (assume it is a point
source) emits a power of 47 microWatts (sound, not electrical). What is the
intensity at a distance of 1 meter from the source
(a) in Watts/m² ? 3.74 x 10-6
W/m2 (b) in db ? 65.7 dB
If the source is 21 meters away, what will
the intensity be
(c) in Watts/m² ? 8.48 x 10-9
W/m2 (d) in db ? 39.3 dB
If the power is doubled from 47 microWatts
to 94 microWatts, what will be the intensity 21 meter away now:
e) in Watts/m2 ? 1.696 x 10-8
W/m2 (f) in db ? 42.3 dB
5) For this problem, assume the speed of
sound in the air around the train and car is 340 m/s. All answers must be at least to the nearest
Hz. Do not round your answers more than
that.
A
train moving West at a speed of 28 m/s approaches a person in a stopped
car.
a) If
the train emits a sound of frequency 4,000 Hz, what will the car observer
measure for the frequency? (Assume no wind.)
4,359
Hz
b) After the train passes the car and starts heading
away (still going West), what will the car observer measure for the frequency?
(Again assume no wind.)
3,696 Hz
c) The car now goes 32 m/s West and
approaches the back of the moving train (which is still going 28 m/s West). If the train again blows its horn (4,000 Hz
with respect to the train), what will the person in the approaching car measure
for the frequency of the horn? (Again assume no wind.)
4,043 Hz
d) ) If
there is a West wind of 18 m/s (from the West blowing toward the East) for part
c, how much will the frequency change
from part c due to the effect of the wind? [a plus difference means the
frequency with the wind will be higher, a minus means it will be lower] ?
-2 Hz .