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SOUND Problems

 

1. What is the period of a sound wave that has a frequency of 2,500 Hz?

2. What is the frequency of a light wave that has a period of 1.6 x 10 -15 sec?

3. What is the wavelength of light in problem #2? (velocity of light =  3 x 108 m/s)

4. What is the wavelength of the sound wave in problem #1?

5. The pendulum in a grandfather clock makes the floor vibrate with a period of 0.5 seconds. What would be the wavelength, in air, of the sound wave generated by this wave?

6. How often does a compression pass an observer who is listening to a sound wave whose length of vibration is 2 ft and a velocity of 1100 ft/sec?

7. A sound wave whose velocity in a particular medium is 600 m/s and has a wavelength of 300 cm. At a certain instant one of the molecules of the medium is at its normal (undisturbed) position in the wave pattern. How much time will elapse before this molecule is again at its normal position in the wave pattern?

8. Many species of bats are known to find their prey by a kind of sonar using short bursts of ultra-sonic waves (waves above the limit of human hearing). What is the wavelength of this wave if the frequency is 50 KHz and the velocity of sound is 1,100 ft/s?

10. What is the shortest and longest wavelength sound that can be heard by a human, if the frequency of audible sound lie between 20 Hz and 20,000 Hz.

11. What is the wavelength of waves broadcast by a TV station whose frequency of transmission is 60 mega-Hz?  

12. A tuning fork is vibrating with a frequency of 550 Hz simultaneously with another tuning fork. Beats at the rate of 2 per second are heard. What two frequency tuning forks may be used to produce these beats?

13. A violin string emits a sound having a frequency of 440 Hz.                                                    

     (A) What is the wavelength of the sound disturbance that passes through the air?

     (B) What is the period of this sound disturbance?

 

14. A tuning fork with a frequency of 600 Hz sends out waves which travel at 1,080 ft/s. How many vibrations does the fork make in the time required for the sound to travel 900 ft?

15. When a sound wave is transferred from one medium to another, its frequency does not change. If the wavelength of a disturbance is 20 cm in air, find its wavelength in:

        (A) water (V = 1,450 m/s)

        (B) steel (V = 5,000 m/s)

       (C) brass (V =3,500 m/s).

 

16. A source of sound sends out waves with a frequency of 500 Hz that travel from air into water. Find the wavelength in each medium (air and water) if the velocity of sound in water is 1,450 m/s?

17. At what temperature would the velocity of sound in air be 370 m/s if it is 331.5 m/s at 0o C? 

18. A timer sets his watch by the report of a gun 100 m away. What is the error recorded on his watch due to the time required for the sound to travel to the timer?

19. A worker strikes the steel rails of a railroad track. A person 1 km away hears two reports, one through steel and the other through the air. What time interval separates the two reports if the air temperature is 10o C   and the velocity of sound in the steel is 5,300 m/s?

20. A workman strikes the rail of a railroad track with a hammer. The sound thus produced reaches the observer through air and steel. The time difference between when he hears the sound through the two mediums is 1 second. If the speed of sound in the steel is 5,300 m/s; how far away is the observer from the worker?

21. The vertical walls of a canyon are 8,800 m apart. A man in the canyon fires a gun and hears the echo from the farther wall 6 seconds after he hears the echo from the near wall. How far is he from each wall?

22. One ship sends signals to a neighboring ship. The sound travels by two paths, air and water. The signals are heard by the neighboring ship at intervals of 6 seconds apart. How far apart are the two ships if the velocity of sound in the water is 1,450 m/s?

23. The limits of hearing of an older person are 40 Hz and 8,500 Hz. Compute the minimum and maximum wavelengths in centimeters in air at 10o C?

24. A submarine detects the presence of an enemy ship by reflected sound waves (sonar). The echo returns in 12 seconds after it was sent when the velocity of sound in water is 1,450 m/s. How far away is the enemy ship?

25. In mapping out the floor of the ocean, a sound wave is reflected back to the surface in 0.8 seconds  when the velocity of sound in water is 1,450 m/s. What is the depth of the water?

26. A clap of thunder is heard 10 seconds after the accompanying lightning flash. How far away is the storm if the air temperature is 10oC?

27. Sound waves pass from air into water in which the velocity of sound is 1,450 m/S. The frequency of  the sound wave is 400 Hz and the air temperature is 0oC. What is the wavelength of this sound in:

      (A) air?

      (B) water?

 

28. A ship lies between a horn buoy and a cliff. An observer on a ship hears the horn buoy 2 seconds after the horn sounded and the echo from the cliff wall 8 seconds after the horn was sounded when the air temperature was 15o C. How far is the ship from:

     (A) the cliff?

     (B) the horn buoy?

 

29. If the ship in problem #28 were on the far side of the buoy from the cliff and all other factors remain constant (temperature and time), how far is the ship from the:

     (A) cliff?

     (B) buoy?

 

30. Two railroad trains approach one another on parallel tracks, each blowing its 500 Hz whistle. The velocity of train “A” is 60 km/hr while “B” is 80 km/hr. An observer travels on a highway that is parallel to the tracks with a velocity of 10 km/hr and the air temperature is 20o C. As they approach and recede from each other, what frequencies will:

      (A) train “A’s” engineer hear [(1); approach (2) recede]

      (B) train “B’s” engineer hear [(1) approach; (2) recede]

      (C) the observer in the car hear [train “A” approaching and receding and train “B” approaching and receding].

 

31. An explosion is seen by an observer 2 seconds before it is heard when the air temperature is 10oC.   How far from the observer did the explosion occur?

32. Calculate the wavelength of the note emitted by a string whose frequency of vibration is 512 Hz when the air temperature is 20oC?

33. A man hunting ducks in the middle of a lake fires his shotgun. Five seconds later he hears an echo from the shore when the air temperature is 10o C.   How far is he from the shore?

34. A gunner stationed 4,500 ft from a cliff fired his gun and heard the echo from the cliff 8 seconds later.

     (A) What was the velocity of sound at this time?

     (B) What was the air temperature?

 

35. A timer at the track meet is standing at the finish line for the 200 m race. He starts his stopwatch with the sound of the starter’s gun when the air temperature is 20oC.

     (A) Will the timer’s watch be fast or slow?   Explain.

     (B) By what factor?

 

36. A man observes a flash of lightning and 6 seconds later hears the thunder when the air temperature is 25oC. How far away was the lightning flash?

37. While working in the field, a farmer sets his pocket watch by the sound of the 12:00 o’clock noon fire siren which is 3 miles away.

     (A) If the air temperature is 16oC, will his watch be fast or slow?

     (B) By what factor?

 

38. A 12 inch air column produces its fundamental resonance with a certain tuning fork when the air temperature is 21oC. What is the frequency of the tuning fork?

39. A closed organ pipe is 8.75 ft in length.

     (A) What fundamental frequency sound will this pipe produce?

     (B) What possible wavelength sound(s) may this pipe produce?

 

40. A uniform flexible 10 m cord carries a wave which is traveling at 18 m/s.

     (A) What fundamental frequency wave could be produced in this cord?

     (B) What is the wavelength of this disturbance?

 

41. A tuning fork makes 1,000 vib/s in air at 20oC. What would be its wavelength in:

     (A) meters?

     (B) ft?

 

42. A vibrator submerged in water produces a 500 Hz sound. The velocity of sound in this water is 4,500 ft/s.

     (A) What is the wavelength of this sound wave?

     (B) If the wave were to have the same frequency in air, what would be its wavelength in air?

 

43. The limits of hearing of a particular person are 32 Hz and 1,600 Hz. When the air temperature is 20oC, what is the:

     (A) longest wave this person could hear?

     (B) What is the shortest wave this person could hear?

 

44. Two hands are clapped together some distance in front of a flat cliff face. The echo returns in 0.25 seconds when the air temperature is 25o C. How far are the hands from the cliff?  

45. The thunder clap of a storm is heard 10 seconds after the accompanying lightning flash when the air temperature is 15oC. How far away is the storm?  

46. A factory whistle has a frequency of 600 Hz. An observer approaching the whistle at a velocity of 60 mi/hr on a day when the temperature is -45oC. What apparent frequencies will he hear as he:

     (A) approaches?

     (B) recedes?

 

47. A man hammers on a steel railroad rail. You hear the sound at your location first thru the rail, then through the air 5 seconds later.  The air temperature is 45oC and the velocity of sound in the rail is 5,400 m/s.  How far are you from the worker?

48. A rifle is fired in a canyon 11,650 m wide with parallel walls. The echo is heard from the far wall 15 seconds after the echo from the near wall on a day when the air temperature is 12oC. How far is the rifle from:

    (A) the near wall?

    (B) the far wall?

 

49. What is the wavelength in meters of the sound produced by a 320 Hz tuning fork when the air temperature is 25oC?

50. What is the frequency of a tuning fork which resonates with a 25 cm long open tube that is 2 cm in diameter when the air temperature is 20oC?

51. How many beats will be heard when a 288 Hz string is simultaneously plucked with a 320 Hz tuning fork?

52. The echo of a ship’s fog horn is reflected from an iceberg and is heard 5 seconds after being sounded. If the air temperature is -35oC, How far away is the iceberg?

53. A rifle is fired in a valley whose parallel walls are 6,800 m apart. An echo is heard from the near wall 5 seconds before the echo from the far wall when the air temperature is 35oC. How far is the rifle from the:

    (A) near wall?

    (B) far wall?

 

54. A worker sets his watch by the sound of a clock in a neighboring town 3 km away on a day when the air temperature is -5oC.   Will he watch be accurate?   Explain.

55. A field judge fires a starters pistol and hears the echo from the bleachers 0.75 sec later when the air temperature is 12oC. How far away are the bleachers?

56. In a laboratory experiment with resonance tubes, we hear resonance produced with a particular tuning fork at the fourth point down the tube. The air temperature is 15oC in the laboratory and the tube is 158 cm long and 2.65 cm in diameter.

     (A) What wavelength sound is heard?

     (B) What is the frequency of the tuning fork being used?

 

57. In an experiment with two closed resonance tubes, we hear the first resonant sound produced with a tuning fork when the air column in each tube is 158 cm in length and the air temperature is (-15oC). The inside diameter of tube “A” is 2.65 cm while tube “B” is 1.85 cm.

    (A) What is the frequency of each tuning fork required for each tube [tube “A” and tube “B”]?

    (B) What will be the number of beats produced from these resonant sounds?

 

58. The vertical walls of a 27,750 m wide canyon are parallel. A man inside the canyon fires a gun and hears the echo from the near wall 4.2 seconds before he hears the echo from the far wall on a day when the air temperature is -22oF. How far is he from the:

    (A) near wall?

    (B) far wall?

 

59. An open pipe 26 cm long and 1.75 cm in diameter is in an environment of  -12oF.

     (A) What are the frequency sounds that are produced for the first three points of resonance?

     (B) What will be the wavelengths of these sounds respectively? 

     (C) Diagram each of these sounds?

 

60. A carpenter is putting a new roof on a house and from where you are watching, you see the hammer at the top of the swing when you hear the sound of the hammer hitting the nail from the preceding swing. The air temperature is 25 oC and the carpenter is swinging at the rate of 2 full swings/sec.    How far away are you from the carpenter?

 

61. A man in a canyon fires a gun and hears the echo from the far wall 5 seconds after he hears the echo from the near wall. The parallel walls of the canyon are 16,580 ft apart and the air temperature is 15o C. How far is he from the:

     (A) near wall?

     (B) far wall?

 

62. You are in the grandstands at the Indianapolis 500 auto race when you observe a car traveling at 180 mi/hr and is emitting a 385 Hz sound. What frequency sound will you hear as he: (A) approaches you? (B) recedes from you?

  Sources of Additional Problems:

        "Physics for Scientists and Engineers" text (Prentice-Hall, Inc., Publisher): Chapter 16 - Sound.  Click on "Practice Questions" in the left window. Answer problems #10, 11, 12, 16, 17, 18, 19, 20, 22, 24, 25.  Also, click on "Practice Problems" #1, 2, 5, 6, 7, 8.

        Physics 1070, University of Guelph, Canada.  Study Guide 2 - Acoustics.  Self Test 3 : Each problem is linked to its solution.  Solve the following problems: #1 (fundamental frequency for an open and closed pipe), #2 (next harmonic for pipes in problem 1), #3 (given numeric values for variables, solve for each pipe's fundamental frequency), #4 (an open pipe problem).  Self Test 4 : Solve the following problems:  #1 (beats and possible frequencies), #2 and #3 (best hearing threshold - solve for basic knowledge).  Self Test 5 : This set involves the intensity, power, and energy associated with sound.  This section may or may not be developed in class this year.  

 

Multiple Choice

1. Sound is caused by objects that:

   (A) reflect                            (C) transmit      

   (B) vibrate                            (D) absorb

 

2. Sound will not travel through:

   (A) air                                 (C) a vacuum

   (B) water                             (D) the Earth

 

3. The pitch of a sound is determined by its:

    (A) vibration rate                 (D) amplitude

    (B) speed                            (E) loudness

    (C) reflection;

 

4. A closed organ pipe will resonate with:

   (A) a node at each end

   (B) a node at the closed end and a loop at the open end

   (C) a node at the open end and a loop at the closed end

   (D) a loop at both ends

 

5. Waves in which the particles of the medium vibrate parallel to the direction of wave motion is called a(n):

    (A) light wave                      (C) transverse wave

    (B) spiral wave                   ( D) longitudinal wave

 

6. Sounds are BEST transmitted in which of the following materials states if their temperatures are the same:

    (A) vapors                           (C) gases    

    (B) solids                             (D) liquids

 

7. If the energy of a sound wave is decreased:

   (A) the frequency increases               (C) the pitch decreases

   (B) the amplitude decreases               (D) the amplitude increases

 

8. The period of vibration is:

   (A) the reciprocal of the frequency                (C) the reciprocal of the amplitude  

   (B) the number of vibrations per second        (D) the reciprocal of the intensity

 

9. When a 45 rpm record is played at 78 rpm:

    (A) the pitch is lowered                                (C) diffraction is produced

    (B) interference is produced                         (D) the pitch is raised

 

10. Two tuning forks that are vibrating simultaneously produce 6 beats/sec.  If the frequency of one of the tuning forks is 256 Hz, then the other one may be:

     (A) 266 Hz                                                (C) 258 Hz

     (B) 262 Hz                                                (D) 254 Hz

 

11. The three properties of a wave that are related to each other in a definite way are:

     (A) wavelength, velocity and energy              (C) wavelength, energy and frequency

     (B) wavelength, velocity and frequency          (D) energy, velocity and frequency

 

12. The Doppler Effect occurs when motion of the source or an observer causes:  

     (A) waves to change in observed frequency

     (B) waves to change their direction of travel

     (C) electromagnetic waves to be slowed

     (D) wave energy to be converted to some other kind of energy

 

13. The speed of sound is affected by all of the following EXCEPT :

     (A) pressure                      (C) volume

     (B) temperature                 (D) density

 

14. When a sound is transmitted from one medium to another, the frequency: 

     (A) is always the same

     (B) is sometimes the same

     (C) is never the same

 

15. One important characteristic of standing waves is:

      (A) their wavelength must be some whole number of their length of travel

      (B) they all move at the same velocity

      (C) is never the same

 

 

 

Matching

 

1. vibration                               A. Uniform frequency pattern

2. echo                                     B. frequencies greater than 20K Hz

3. pitch                                     C. maximum deflection of the medium particles

4. noise                                     D. uneven frequency patterns  

5. musical sound                        E. multiple reflections

6. ultrasonic                               F. reflected waves

7. loudness                                G. forced vibrations caused by a source of sound

8. resonance                              H. will not transmit sound

9. vacuum                                  I. moving object causing sound

                                                  J. determined by frequency

                                                 K. determined by energy put into the sound