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1.13 PRACTICE QUESTIONS
À pS1. What is the frequency of a wave with a wavelength in air of 0.026m at 10°C (in air)? (ans. 12973 Hz)
S2. What is the sound power radiated by a machine with specified sound power level (Lw) of 130 dB? (ans. 10 W)
S3. Three machines of equal sound power are to be placed next to two existing machines each having sound power levels of 82dB. It has been determined that the combined sound power of all 5 machines must not exceed 63mW. What maximum sound power level must each of the new machines be limited to? (ans. 103.2dB)
S4. A cylindrical tube is to be used for sound propagation tests with a loudspeaker located at one end pointing down the tube. The range of test frequencies to be examined is from 300Hz to 3000Hz under temperature extremes of 5 degrees Celsius to 25 degrees Celsius. Determine the minimum tube length to ensure one full wavelength at the lowest frequency and the maximum diameter to limit the highest frequency transverse (across the tube) wave to one half wavelength. The above to hold for all temperature extremes. (ans. L=1153mm, D=55.7mm)
S5. Given the loud speaker test results given below, (ans. Q=1.35)
S6. The following data was recorded for a non-isotropic source. What would be the directivity factor (Q) in direction q = 60° (use appropriate approximation for calculation of the average value). (ans. 0.7)
S7. You are given two loudspeakers to be mounted in the passenger section of a commercial aircraft. For testing, a speaker is mounted in a test setup, and powered with a 40 watt stereo. Measurements are taken at the points listed below. From the data, a) calculate dB pressure level for each measurement, b) calculate directivity for each point, c) calculate the total power, and d) select the speaker best suited to the application (or neither) and explain your choice.
S8. What will be a) the total sound power level of 5 machines rated as follows 93dB, 91dB, 89dB, 92dB, 88dB. b) If the least noisy machine is turned off, by how much does the dB power level drop? (ans. a) approx. 98dB, b) -0.5dB)
S9. Three machines are individually measured against a background level of 78 dB. Sound pressure levels are 83dB, 81dB, 80dB. What would be the total sound pressure level with all three machines on at a new location where the background level was 80dB? (ans. 85.3dB)
S10. Calculate the average sound pressure levels for the following recorded values: 89dB, 93dB, 97dB, 85dB, 92dB. (ans. 92.9dB)
S11. Two identical sources have a combined amplitude (Lp) of 104dB. What would be the value of the root mean square pressure for just one of the sources? (ans. 2.24Pa)
S12. The sound pressure level measured at a distance of 3m from a machine including background noise was recorded as 96dB. The ambient level was then measured with the machine off and found to be 93.4dB at the same location. If the ambient level was to be raised by 2dB what would the combined machine and background level at the same measurement location? (ans. 97.2dB)
S13. Given a set of three sound pressure measurements (.05Pa, .03Pa, .04Pa) taken at 1/2 Octave intervals, starting at 200 Hz, find the total loudness in sones.
S14. A machine has a loudness rating of 35 sones, what will be the loudness level (phons) - give approximate (graphical) and exact (calculated) answers. (ans. 91.4 phons)
S15. Based on a limited one octave (1/1) analysis calculate the loudness in sones for the following noise and loudness level. (ans. 43.9 sones)
S16. You have been approached by a business that has just signed a 5 year lease for office space. But, they want to cancel the lease because they claim the background noise is too great for an office. You enter the building and take some readings at every octave from 100Hz. The values you get are 35dB, 42dB, 48dB, 42dB, 35dB, 31dB. Is the sound level suitable for office space?
S17. For the same spectrum as in #S15, calculate the NC rating (use the graph). (ans. NC > 65)
S18. Using the graph to calculate the total level in dBA for the same spectrum. Use fig 2.8 (A-weighted curve) to find dBA levels then add. (ans. approx. 85 dBA)
S19. You have decided to quit engineering, and go into the restaurant business. And, your new concept is to design an environment where the patrons don't have to shout. You are using 5 foot round tables throughout the room, with a 1000W sound system that gives even music throughout your establishment. a) Calculate the general range of pressure levels from 500Hz to 2000Hz that would interfere with shouting. b) Calculate the general range of pressure levels from 500Hz to 1000Hz that would interfere with normal speech.
S20. The sound pressure readings below were taken at 1/3 octave intervals beginning at 500 Hz; 54, 72, 89, 87, 92, 94, 95, 104, 88, and 74 dB. These readings were taken in the same room that houses 3 workers. We must determine if the room sound levels are safe.
e) What is the farthest distance apart and two workers may be to hear each other shouting using PSIL and background dBA? (ans. 2ft for both)
S21. The Shoutalot Sound Measurement Company was hired to determine if an assembly shop was safe for the workers at the Rustyheap Car Company. To do this they took sound measurements and found that the workers were right at the safety limit (i.e. D = 1). But before the report was completed, Mr. I.M. Kluzt, P.E., lost the sheets of paper that the measurement data was on. But he remembered that 3 hours of the 7 hour shift are at 95 dBA. You must estimate what the sound level was for the other 4 hours of the shift (the additional 4 hours were all at the same level). (ans. 85 dBa max.)
S22. At the perimeter of a local fast food restaurant you find the noise levels are 60dBA from 2am to 8am, from 8am to 8pm the noise level goes up to 75dBA, and from 8pm to 2am the noise level goes down to 70dBA. Assuming this has a 10 dBA night-time noise penalty from 10pm to 7am, calculate the noise pollution level.
S23. a) A worker has been exposed to noise levels over a period of 5 hours as listed below. For what remaining portion of his 8 hour shift could he be exposed to a level of 90 dBA. (ans. 1hr 20min)
b) Based on a daytime Leq of 60dBA and a nighttime level of 45dBA, what would be the Ldn index for the entire day? (ans. 58.7dBA)
S24. The sound spectrum below is known to exist for an industrial machine. Keeping in mind the proximity of some of the peaks, what bandwidth would our sound instrumentation require to tell them apart? (ans. 1 octave?)
S25. For a 1/12 octave band pass frequency analyzer what would be the percentage (B.W./f0) and the upper and lower cutoff frequencies at f0=12000Hz. (ans. 5.78%)
S26. A 1/10 octave bandpass filter has a centre frequency of 5000Hz. Calculate the half power bandwidth cutoff frequencies (f1, f2) and the local attenuation of a pure tone signal at 6000Hz by this filter.(ans.
S27. The Bouncy Rubber company uses a 100 horsepower air compressor and an exhaust fan when making vulcanized rubber balls. The axial fan creates a flow of 5 m3/sec at a pressure of 200 mmHg. The (10' by 10' by 10') room they are housed in has walls of concrete blocks painted red.
S28. A generator room contains an average 500 h.p. diesel motor (the sound is about 1000Hz). The ceiling and walls of the (3m by 3m by 3m) room are covered in plaster and the floor is concrete. On one wall there is a 2m by 2m window. If the generator is in one corner of the room, and you are in the other corner, what sound pressure will you hear (in Pascals)? (ans. 11.3 Pa)
S29. Acoustic Ohm's law for freely propagating states that,
S30. A machine is located at position A and radiates 0.6W of sound power in the octave band centered at 1000Hz with a directivity of 1.6 in the direction of an observer at location B. The machine is operated for each 8 hour shift. There is a second machine located at position C which is used infrequently. It radiates a sound power of 0.2W with a directivity of 1.0 in the same frequency range.
a) calculate the total direct sound pressure level at position B with both machines on (i.e., ignoring the reverberant field effects). (ans. 90.0 dB)
b) calculate the average absorption coefficient and the room constant in this frequency range (use the table in the notes for component values). (ans. 0.410, 263 sq.m.)
c) calculate the sound pressure level at position B with only machine A on taking room effects into consideration. (ans. 100 dB)
S31. The company would like to reduce the sound pressure level at the operator location and is considering laying foam backed carpet (a = 0.69) on 75% of the floor surface. What would be the new sound pressure level at position B, machine A on under these conditions. (ans. 101 dB)
S32. Predict the expected sound pressure level at a location 3m from a source radiating 100dB of sound power, assume isotropic radiation (spherical) and in a sound absorbing room. If the actual reading at this location was 83dB, what would be the Directivity Factor (Q) be? (ans. Lp=79.47dB, Q=2.256)
Note: the equation you use in the first part of this question is derived from the relationship (i) the directivity of the source modifies the numerator of this expression (ii).
S33. Under free field conditions the sound pressure level of a noise source was measured and found to be 88dB at a distance of 4m. Assuming isotropic radiation what would be the sound power level (Lw) of the source? (ans. 111dB)
S34. a) If an enclosure was made from 3/4" thick plywood to fit over the noise source in S30, what internal treatment would be required to ensure an insertion loss of 21dB. (ans. a>= .251)
b) For the room described in S30 assume acoustic treatment is applied to raise the average absorption coefficient to 0.40. What time would be required for the sound energy density to reach 60% of it's steady state value after the machine was switched on? (ans. .02sec)
c) A noise source is located in anechoic free space and emits 1.5W of sound power. A sound level meter is located 3m from the source and the directivity factor in this direction is 4. Calculate the expected sound pressure level and derive the average sound pressure level at a radius of 3m from the machine. (ans. 101.18dB)
S35. The Boris and Natasha Detective Agency has hired you to build soundproof walls between their interrogation rooms. The dimensions and location of the two rooms are shown below. The loudest voice in either room will be 80dB, and a listener can hear voices at pressure levels above 20dB. What materials should be used for the wall?
S36. In another study the company decides to investigate the benefit of making a separate room to contain machine A and program machine B to run unattended after hours. A door between the two rooms would not be necessary, however a 1m by 2m window is considered essential (this would be heavy plate glass to reduce transmission losses a=0.03 and TL=40dB at 100Hz). The broken line shows the intended separation line which would be a 2" by 4" stud wall with 0.5" (6 lbs/ft) gypsum panels on both sides (a = 0.05 and TL = 40dB at 1000Hz). What would be the new sound pressure level at position B with the machine on and the wall in place. Assume reverberant field conditions (Lp3).
S37. The room pictured below is made from standard construction materials as noted. The machine radiates 2W of acoustic power isotropically in the octave band centered at 500Hz.
a) calculate the steady state space average sound energy density for the room. (ans. 3.213*10-4 J/m3)
c) without doing the actual calculations, explain how you would go about determining the sound pressure level at point #2, just outside the exterior west wall. (ans.)
S38. (See figure below) The elevation and plan views of a room are shown. A barrier is to be installed. The location and height have been determined. The required insertion loss considering diffraction paths only is to be 5dB. The absorption coefficients in the octave band centered at 500Hz are .70, .30, .05 for the ceiling, walls and floor respectively. The printer generates a sound power level of 110 dB and in the direction of the worker location has a directivity factor of 1.9. Calculate the barrier length necessary to ensure the required insertion loss. (ans. L=3.57m)
S39. You think that a bend in a narrow hallway of your house reduces noise levels. This "plenum" has the dimensions below. Determine the Transmission Loss for 500 Hz.
S40. For the same noise in #S15 calculate the total perceived noise (PN) and perceived noise level (PNL) (ans. PN=54.1 noys, PNL = 97.7 PNdB)
S41. The S.Butts Manufacturing company produces large castings. Seymour, the division director has asked that the Engineering department take sound readings about a large machine. The engineers make the following measurements with the machine turned off, then on.
S42. A large incinerator is located in the centre of a residential neighborhood. Inside the facility the measurements are made of general background noise, these are listed below. Measurements are also made outside over a 24 hour period at the perimeter of the facility.
e) If the local municipality has an 11pm to 6am noise penalty of 15dB, what is the noise pollution level, and the Ldn?
S43. A room, 8' high by 10' by 20' has painted concrete floors, painted concrete walls, and an unpainted concrete ceiling. If a 100hp electric motor (1200rpm) is in one end of the room,
S44. We take measurements about a sound source and get the following table (except the missing value). Using the following relationship, and the table of values, find the missing value.
S45. A sound is measured in octave intervals starting at 115 Hz. The pressure level values measured (in order of frequency) are given below. Find the total loudness in noys. (for octaves K= 0.3)
S46. A recent observation has revealed that an older type of beverage, commonly known as a `shooter', has become popular in an previously unexplored market. As a result you decide to cash in on the trendy new happening and cater to this niche market. To keep the patrons drinking, you plan to play the music loud, but if it is too loud the waiting staff will not be able to hear the somewhat intricate orders. You have decided that in the worst case the patron will have to shout over a maximum distance of 3 feet. Tests on the music system reveal that the sound has a fairly constant level, except near 1000 Hz, where it always seems to be 20dB above all of the other frequencies. If we set the volume level of the music system using a sound pressure meter that is set to 500Hz, what is the ideal reading on the sound meter?
S47. A design is specified so that it should have a maximum preferred noise criteria value of 35. When tested, the sound values measured at half octaves from 63Hz are,
At what frequencies are the sounds measured above tolerance, and which sound frequency is the worst violator. Use the graph and clearly indicate how you arrived at your solution.
S48. The S.Butts Manufacturing company produces large castings. Seymour, the division director has asked that the Engineering department take sound readings about a large machine. The engineers make the following measurements with the machine turned off, then on.
S49. A large incinerator is located in the centre of a residential neighborhood. Inside the facility the measurements are made of general background noise, these are listed below. Measurements are also made outside over a 24 hour period at the perimeter of the facility.
e) If the local municipality has an 11pm to 6am noise penalty of 15dB, what is the noise pollution level, and the Ldn?
S50. A room, 8' high by 10' by 20' has an unpainted concrete floor, painted concrete block walls, and an unpainted concrete ceiling. If a 100hp electric motor (1200rpm) is in one end of the room and whines at 990Hz,
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