1. 1) A piano emits frequencies that range from a low of about 26 Hz to a high of about 4250 Hz. Find the range of wavelengths spanned by this instrument. Assume the speed of sound in air to be 345 m/s.

2. 2) A sound wave traveling at 347 m/s is emitted by the foghorn of a tugboat. An echo is heard 3.55 seconds later. How far away is the reflecting object?
d = v • t
d round trip = (347 m/s)(3.55 sec) = 1232 m
d to wall = 616 m

3. 3) A string under a tension of 100 N has a wave on it traveling at 90 m/s. What is the speed of a wave on this string if the tension is doubled?
For a constant 
V2 = 127 m/s

4. 4) Katie and Katie have lost Travis while hiking in the woods
4) Katie and Katie have lost Travis while hiking in the woods. They yell out "TRAVIS!" and hear an echo 2.6 seconds after they shout. If the temperature is 27° C, how far away is the mountain that reflected the sound wave?
Find the speed at 27oC
d = v • t = (347 m/s)(2.6 sec) = 902 m
d = ½ (902) = 451 m

5. 5) A rock group is playing in a bar
5) A rock group is playing in a bar. Sound emerging from the door spreads uniformly in all directions. If the intensity level of the music is 80.0 dB at a distance of 5.0 m from the door, at what distance is the music just barely audible to a person with a normal threshold of hearing?
R2 = 50,000 m
I = 10-4 W/m2

6. Observer is moving toward the source
6) At rest a car's horn sounds the note A (440 Hz). While the car is moving down the street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car's speed hears the note A-flat (415 Hz). How fast is the car moving? Is the cyclist ahead of the car or behind the car?
Observer is moving toward the source
Source is moving away from observer
V = 32.8 m/sec

7. 6) At rest a car's horn sounds the note A (440 Hz)
6) At rest a car's horn sounds the note A (440 Hz). While the car is moving down the street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car's speed hears the note A-flat (415 Hz). How fast is the car moving? Is the cyclist ahead of the car or behind the car?
0.943(345+v) = v/3
V = 32.8 m/sec

8. 7) A stretched string is 160 cm long and has a linear density of 0
7) A stretched string is 160 cm long and has a linear density of g/cm. What tension in the string will results in a second harmonic of 460 Hz?
First Harmonic

9. 7) A stretched string is 160 cm long and has a linear density of 0
7) A stretched string is 160 cm long and has a linear density of g/cm. What tension in the string will results in a second harmonic of 460 Hz?
= 1.60 m
First Harmonic
V =  f = (1.60m)(460 Hz)
= 736 m/s
F = 813 N
Second Harmonic

10. 8) A wire of mass 0.3 g is stretched between two points 70 cm apart.
A) If the tension in the wire is 600 N, find the first, second, and third harmonics of this string.
0.70m (1/2 )
0.70m (1/2 )
Fundamental  = 1.40m

11. 8) A wire of mass 0.3 g is stretched between two points 70 cm apart.
B) To what tension would the wire have to be stretched in order for the frequency of the fundamental (first harmonic) to be 20,000 Hz?
V = f •  = (20,000)(1.40) = 28,000 m/s
C) Does it seem likely that this could be accomplished? No

12. 9) A pipe open at both ends has a fundamental frequency of 300 Hz when the temperature is 0°C. (a) What is the length of the pipe? (b) What is the fundamental frequency at a temperature of 30°C? B.
f1 = 300 Hz
L = 0.552m

13. 10) A piano tuner strikes a 440 Hz tuning fork at the instant she strikes a piano key that should emit a tone of 440 Hz and hears a beat frequency of 2 Hz. What are the possible frequencies the piano key could be emitting?
440  2 = 438 , 442

14. 11) A commuter train passes a passenger platform at a constant speed of 40 m/s. The train horn is sounded at a frequency of 320 Hz when the train is at rest. (a) What is the frequency observed by a person on the platform as the train approaches and (b) as the train recedes from hi m? (c) What wavelength does the observer find in each case?
a. Train moves towards observer…
b. Train moves away from observer…

15. 11) A commuter train passes a passenger platform at a constant speed of 40 m/s. The train horn is sounded at a frequency of 320 Hz when the train is at rest. (a) What is the frequency observed by a person on the platform as the train approaches and (b) as the train recedes from hi m? (c) What wavelength does the observer find in each case? c.

16. 12) A pipe open at each end has a fundamental frequency of 300 Hz when the speed of sound in air is 333 m/s, (a) What is the length of the pipe? (b) What is the frequency of the second harmonic when the temperature of the air is increased so that the speed of sound in the pipe is 344 m/s?
For the second harmonic… L =  A. B.
L = 0.555m

17. For the second harmonic… L =  A. B.
12) A pipe open at each end has a fundamental frequency of 300 Hz when the speed of sound in air is 333 m/s, (a) What is the length of the pipe? (b) What is the frequency of the second harmonic when the temperature of the air is increased so that the speed of sound in the pipe is 344 m/s?
For the second harmonic… L =  A. B.
Fundamental
L = ½ 
Second Harmonic
L = 
L = 0.555m

18. 13) A string of 8.0 g mass and 5.0 m length has one end attached to a wall while the other end is draped over a pulley and attached to a hanging mass of 4.0 kg. If this string is plucked, what is the fundamental frequency of vibration?
5 m
.008 kg
4 kg

19. 14) A typical sound level for a buzzing mosquito is 40 dB, and normal conversation is approximately 50 dB. How many buzzing mosquitoes will produce a sound intensity equal to that of a normal conversation?
10 dB = 10 times change in Intensity… so, you’ll need 10 mosquitoes.
OR…
Now, find I for many mosquitoes …
Find I for 1 mosquito…

20. 15. A spring is hung from the ceiling, and an object is attached to the lower end stretches the spring a distance of 5.00 cm from the un-stretched position. If the spring constant is 47.5 N/m, what is the mass of the object?
F = 0
Fs = Fg
-kx = -mg
-(47.5)(0.05) = -m(9.8)
m = kg

21. 16. A simple 2.00 m long pendulum oscillates at a location where g = 9.80 m/s2. How many complete oscillations does it make in 5.00 min?

22. 17. A 3.5 m long pendulum clock that works perfectly on Earth is taken to the moon. Will it run fast or slow there? What is the period of the clock on the moon where the free fall acceleration is 1.63 m/s2?
Slower.