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 .