PHYS 201 TEST #5 12/9/16
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 1,500 grams pulls down on a spring which stretches 6_{ }cm from
its original unstretched position due to the
weight.

a) What is the spring
constant, k, of the spring?

**245 Nt/m**

b) If this mass is stretched
a further 2_{ }cm from the equilibrium position (which will be 8 cm
from its original unstretched position) and then
released, it will oscillate. What will be the period, T, of its oscillation?

**0.49 sec**

c) What will be the frequency of this
oscillation?

**2.03 Hz.**

d)
If the amplitude is increased from 2 cm to 3 cm, that is, the spring is
stretched 9 cm from the unstretched position and then
released, will the period of oscillation [decrease, stay the same, or
increase]?

**stay the same**

e) For the same spring, if a mass of 2,000 grams
is used with the spring so that bigger mass stretches the spring a little more
than 6 cm from its original position, and the spring is stretched 2 cm from its
new equilibrium position (amplitude remains at 2 cm), will the period of
oscillation [decrease, stay the same, or increase]?

**increase**

f) If the original 1,500
grams mass is used (from parts a-c), but a new spring with a smaller spring
constant is used, assuming the amplitude remains at 2 cm, will the period of
oscillation [decrease, stay the same, or increase]?

**increase**.

2) A certain string has a
length of 0.60 meters and a mass density of 0.8 grams/meter. A tension of 25 Nt is applied to it.

a) What will be the speed of
the wave on this string?

**177 m/s**

b) What will be the
fundamental frequency when it is plucked?

**147 Hz.**

c) If a second string of the
same length and same tension is to be used but a fundamental frequency half
that of part b is desired, what should the mass density of this second string
be?

**3.2 grams/meter.**

d) If the original string of
parts a & b is used, and if a frequency is 240 cycles/sec is desired,
should the tension for this string be [lower, the same, or higher] than the
original 25 Nt?

**higher**.

3) a) What is the speed of
sound in air that is at a temperature of 41^{o}F ?

**334 m/s**

b) What is the frequency of a
60 cm wavelength sound wave in this air?

**556 Hz.**

c) What is the wavelength of
a 240 Hz sound wave in this air?

**1.39 m. **

d) If the temperature of this
air were lower and the frequency of the sound wave were kept the same, would
the wavelength of the sound wave [decrease, stay the same, or increase] ?

**decrease**

e) If helium (molar mass of
helium is 4 gm/mole, and helium is a monatomic gas, not a diatomic gas like N_{2}
and O_{2}) 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 400 nanoWatts (sound, not
electrical). What is the intensity at a distance of 1 meter from the source

(a) in Watts/mē ? **3.18 x
10 ^{-8} W/m^{2}** (b) in db ?

If the source is 25 meters
away, what will the intensity be

(c) in Watts/mē ? **5.09 x
10 ^{-11} W/m^{2}** (d) in db ?

If the power is doubled from
400 nanoWatts to 800 nanoWatts,
what will be the intensity 25 meter away now:

e) in Watts/m^{2} ? **1.02
x 10 ^{-10} W/m^{2} **(f) in 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 25 m/s approaches a person in a stopped
car.

a)
If the train emits a sound of frequency 6,000 Hz, what will the car observer
measure for the frequency? (Assume no wind.)

**6,476 Hz**

b) A second observer is in a car heading
West at a speed of 35 m/s towards the back of the train; what will the 2^{nd}
car observer measure for the frequency? (Again assume no wind.)

**6,664 Hz**

c) The 2nd car,
still going 35 m/s West, now passes the train, still going 25 m/s West, and the
train again blows its horn (6,000 Hz with respect to the train). What will the person in the 2nd car now
measure for the frequency of the horn? (Again assume no wind.)

**5,810 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] ?

**+8 Hz** .