PHYS 201 TEST
#5 12/7/12 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 8 cm from its original unstretched position
due to the weight.
a) What is the spring constant, k, of the
spring?
49 Nt/m
b) If this mass is stretched 2 cm
from the equilibrium position (which will be 10 cm from its unstretched
position) and then released, it will oscillate. What will be the period, T, of
its oscillation?
0.57 sec
c) ) If the amplitude is increased from 2 cm to 3 cm, that is,
the spring is stretched 11 cm from the unstretched 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 4 cm (half the
original 8 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-c), but the mass that is oscillating is decreased from 400 grams to 300
grams, assuming the amplitude remains at 2 cm, will the period of oscillation
[increase, stay the same, or decrease]?
decrease.
2) A certain guitar string has a length of
0.42 meters and a mass density of 0.67 grams/meter. A tension of 32 Nt. is
applied to it.
a) What will be the speed of the wave on
this string?
218.5 m/s
b) What will be the fundamental frequency
when it is plucked?
260.2 Hz.
c) If a fundamental frequency of 220 cycles/sec (note A4) is desired, what should the
tension in the string be?
22.9 Nt.
d) If a different string of the same length
but a larger mass density is used, and if the desired frequency is 220
cycles/sec (same note as in part c), should the tension for this string be
[higher, the same, or lower] than for the string in part c)?
higher.
3) a) What is the
speed of sound in air that is at a temperature of 23oF ?
327.7 m/s = 734 mph.
b) What is the frequency of a 75 cm
wavelength sound wave in this air?
436.9 Hz
c) What is the wavelength of a 440 Hz sound
wave in this air?
0.745 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 250 nanoWatts (sound, not electrical). What is the
intensity at a distance of 1 meter from the source
(a) in Watts/m² ? 2.0
x 10-8 W/m2 (b) in db ? 43.0
dB
If the source is 123 meters away, what will
the intensity be
(c) in Watts/m² ? 1.31
x 10-12 W/m2 (d) in db ? 1.2
dB
If the power is doubled from 250 nanoWatts
to 500 nanoWatts, what will be the intensity 123 meter away now:
e) in Watts/m2
? 2.63 x 10-12 W/m2 (f) in db ?
4.2 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 East at a speed of 20 m/s approaches a person in a stopped
car.
a) If
the train emits a sound of frequency 5,000 Hz, what will the car observer
measure for the frequency? (Assume no wind.)
5,312.5
Hz
b) After the train passes the car and starts heading
away (still going East), what will the car observer measure for the frequency?
(Again assume no wind.)
4,722 Hz
c) If the car now goes 30 m/s East and
approaches the rear of the moving train (which is still going 20 m/s East) and
the train again blows its horn (5,000 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.)
5,139 Hz
d) ) If
there is an East wind of 15 m/s (from the East blowing toward the West) 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] ?
-6 Hz .