PROBLEMS

Back

2-1. In the 200-meter track event, the starter is located a distance of

150m (492.1 ft) from the timers. If the air temperature is 228C

(295.2K or 71.68F), how long does it take the sound of the starter’s

gun to reach the timers? The gas constant for air is 287 J/kg-K and

the specific heat ratio _ ј 1:400.

2-2. One proposed type of thermometer is one that measures the speed of

sound in an ideal gas. If this thermometer indicates a speed of sound

in methane gas рR ј 518:4 J/kg-K; _ ј 1:299) of 425 m/s (1394 ft/

sec), determine the temperature of the methane gas.

2-3. Sonic liquid level gauges are used to measure the liquid level of

liquids in closed containers. Such a gauge is installed in a water

container, and the transducer is placed at the bottom of the container.

The sound pulse emitted from the transducer moves through

the liquid, is reflected at the liquid surface, and travels back to the

transducer. If the water temperature is 208C (688F) and the total

transit time of the sound pulse is 10 ms, determine the level of liquid

water in the container.

2-4. For gold, Young’s modulus is 75 GPa (10:88 _ 106 psi), Poisson’s

ratio is 0.42, and the density is 19,320 kg/m3 (1206 lbm=ft3).

Determine the bulk speed of sound in gold.

2-5. The wavelength of a sound wave is 305mm (12.0 in). Determine the

frequency and wave number for a plane sound wave propagated in

(a) air at 208C (293.2K or 688F), R ј 287 J/kg-K, _ ј 1:400 and (b)

helium at 208C, R ј 2078 J/kg-K, _ ј 1:667.

Basics of Acoustics 37

Copyright © 2003 Marcel Dekker, Inc.

2-6. A famous basketball player has a height of 2.110m (6 ft 11 in). At

what frequency would a sound wave in air at 258C (298.2K or 778F)

have a wavelength equal to the player’s height?

2-7. A trombone produces a plane sound wave having a frequency of

170 Hz and a rms acoustic pressure of 13.1 Pa in air at 258C

(298.2K or 778F) and 101.3 kPa (14.7 psia). Determine the rms

acoustic particle velocity for the sound wave.

2-8. A plane sound wave is propagated in air at 158C (288.2K or 598F)

and 101.3 kPa (14.7 psia). The intensity of the wave is 10mW/m2.

Determine the rms acoustic pressure, the rms acoustic particle velocity,

and the acoustic energy density for the sound wave.

2-9. A spherical source of sound radiates uniformly into a large volume

of air at 228C (295.2K or 728F) and 101.3 kPa (14.7 psia). The frequency

of the sound wave is 274 Hz, and the acoustic power radiated

from the source is 30mW. At a radial distance of 500mm (41.7 in)

from the source, determine the intensity, the rms acoustic pressure,

the rms acoustic particle velocity, and the acoustic energy density.

2-10. When Bix Beiderbecke, the talented jazz performer of the 1920s,

played a high G on his cornet (concert F pitch), he produced a

note having a frequency of 690.5 Hz, and the resulting sound

waves could be treated as spherical waves (for this problem). At a

distance of 60.5mm (2.38 in) from his cornet, the rms acoustic particle

velocity was 2.60 mm/s (0.102 in/sec). The warm air in his club

was at 328C (305.2K or 908F). Determine the rms acoustic pressure

and acoustic intensity at a distance of 60.5 mm from Bix’s cornet

when he played the high G.

2-11. An acoustic quadrupole source radiates sound with an acoustic pressure

distribution function given by:

Hр_Ю ј 1

2 р3 cos2 _ _ 1Ю

Determine the expression for the directivity factor and directivity

index for this symmetrical directional source along the axis, _ ј 0.

2-12. An acoustic triplet source radiates sound with an acoustic pressure

distribution function given by:

Hр_Ю ј 1

2 р1 ю cos _Ю

Determine the expression for the directivity factor and directivity

index for this symmetrical directional source along the axis _ ј 0,

and for _ ј 608.

2-13. A boiler feedwater pump radiates sound as a spherical source. The

acoustic power level for the pump is 103 dB, and the frequency of the

38 Chapter 2

Copyright © 2003 Marcel Dekker, Inc.

sound wave is 63 Hz. The sound travels through air at 36.88C (310K

or 98.28F) and 101.3 kPa (14.7 psia). At a distance of 1.50m (4.92 ft)

fromthe pump, determine (a) the intensity and intensity level and (b)

the energy density and energy density level for the sound.

2-14. A plane sound wave is propagated in the water in a pipe having an

internal diameter of 100mm(3.937 in) and a length of 30m(9.144 ft).

The properties of the water are density 1000 kg/m3 and sonic velocity

1400 m/s. The intensity level for the sound wave is 121 dB. Determine

(a) the sound pressure level, (b) the acoustic particle velocity, and (c)

the total acoustic energy (mJ) contained in the water in the pipe.

2-15. A chain saw produces a spherical sound wave having a frequency of

214Hz in air at 358C (308.2K or 958F). At a distance of 600mm

(23.62 in), the sound pressure level is 100 dB. Determine (a) the

acoustic power level and (b) the rms acoustic particle velocity and

velocity level at a distance of 600mm from the saw.

2-16. When two pumps are both operating, the sound pressure level at a

distance of 10m from the pumps is 101.8 dB. When pump A is

turned off (only pump B operating), the measured sound pressure

level at 10m from the pumps is 97.0 dB. Determine the sound pressure

level when pump B is turned off and only pump A is operating.

The sound waves are radiated through air at 228C (205.2K or 728F)

and 101.3 kPA (14.7 psia).

2-17. The sound pressure level spectrum around a wood chipper unit is

given in Table 2-6. Determine (a) the overall sound pressure level

and (b) the A-weighted sound level for the chipper noise.

2-18. A machine produces the sound pressure level spectrum in octave

bands at a distance of 3m (9.84ft), as given in Table 2-7.

Determine the overall sound pressure level and the A-weighted

sound level at 3m from the machine.

Basics of Acoustics 39

TABLE 2-6 Data for Problem 2-17

Octave band center frequency, Hz

63 125 250 500 1,000 2,000 4,000 8,000

Lp(OB), dB 91 88 99 102 99 98 98 88

Copyright © 2003 Marcel Dekker, Inc.

Навигация