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 41oF ?

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 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 400 nanoWatts (sound, not electrical). What is the intensity at a distance of 1 meter from the source

(a) in Watts/m² ? 3.18 x 10-8 W/m2 (b) in db ?  45.0 dB

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

(c) in Watts/m² ? 5.09 x 10-11 W/m2 (d) in db ? 17.1 dB

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

e) in Watts/m2 ? 1.02 x 10-10 W/m2 (f) in db ? 20.1 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 2nd 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 .