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.

mHz

mHz

f

v

m

High

m

Low

0812.04250

345

3.1326

345

sec

sec

==

==

=

λ

λ

λ

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) 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?

μF

v = For a constant μ

2

190

22

1

2

1 ==vF

Fvv

V2 = 127 m/s

Fv α

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?

sec347273

271331

2731331

m

Tv

=

+=

+=d = v • t = (347 m/s)(2.6 sec) = 902 m

d = ½ (902) = 451 m

Find the speed at 27oC

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?

1210log1080 −=

I

1210log8 −=

I

128

1010 −=

I

I = 10-4 W/m2

21

22

2

1

R

R

I

I=

2

22

12

4

510

10 R=−

−

R2 = 50,000 m

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?

€

f ' = fvwave

+vobserver

vwave

−−vsource

⎛

⎝ ⎜

⎞

⎠ ⎟

V = 32.8 m/sec

Observer is moving toward the source

Source is moving away from observer

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?

⎟⎟⎠

⎞⎜⎜⎝

⎛

++

=sourcewave

observerwave

vv

vvff '

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

+=

v

v

3453

345440415

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+

+=

v

v

3453

345

440

415

0.943(345+v) = 345 + v/3

V = 32.8 m/sec

7) A stretched string is 160 cm long and has a linear density of 0.015 g/cm. What tension in the string will results in a second harmonic of 460 Hz?

First Harmonic

7) A stretched string is 160 cm long and has a linear density of 0.015 g/cm. What tension in the string will results in a second harmonic of 460 Hz?

Second Harmonic

λ= 1.60 m

mkg

cmg

m

cm

g

kg0015.

1

100

1000

115.0 =⎟⎟

⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

μ

V = λ f = (1.60m)(460 Hz)

= 736 m/s

0015.736

FFv ==

μ

F = 813 N

First Harmonic

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 λ)Fundamental λ = 1.40m

mkg

m

kg000429.

70.0

0003.==μ

sm

NFv 6.1182

000429.

600===

μ

Hzv

f 84540.1

11831 ===

λHzfHzf 25351690 32 ==

0.70m (1/2 λ)

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 • λ = (20,000)(1.40) = 28,000 m/s

NF 51036.3

000429.000,28 ×==

C) Does it seem likely that this could be accomplished?

No

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?

f1 = 300 Hz

L

L

vnfn

2

3311300

2

=

=

L = 0.552m

B.

smv 349

273

301331 =+=

Hzfn 316)552(.2

3491 ==

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

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…

Hzf 36240345

0345320 =⎟

⎠

⎞⎜⎝

⎛−±

=

b. Train moves away from observer…

Hzf 28740345

0345320 =⎟

⎠

⎞⎜⎝

⎛+±

=

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. mf

vA 953.0

362

345===λ

mf

vB 200.1

287

345===λ

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?

A.

L

L

vnfn

2

3331300

2

=

=

L = 0.555m

B. For the second harmonic… L = λ

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?

A.

L

L

vnfn

2

3331300

2

=

=

L = 0.555m

B. For the second harmonic… L = λ

Fundamental

L = ½ λ

Second Harmonic

L = λ

Hzf

L

vnfn

620)555(.2

3442

2

2 ==

=

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?

4 kg

5 m.008 kg

mkg

m

kg0016.

5

008.==μ

sm

Fv 157

0016.

)8.9(4===

μ

mL 102 ==λ

Hzm

vf

sm

7.1510

157===

λ

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.

Find I for 1 mosquito…

1210log10 −=

Iβ

28

12

10

10log1040

mWI

I

−

−

=

=

Now, find I for many mosquitoes …

27

12

10

10log1050

mWI

I

−

−

=

=

1010

10#

8

7

1

=== −

−

II

mosquitoes many

OR…

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 = 0.242 kg

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?

€

T = 2πLg

= 2π2

9.8= 2.84 sec/rev

€

2.84rev1sec

×60sec1min

×5min

= 852rev

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?

€

T = 2πLg

= 2π3.5

1.63= 9.2 sec/rev