Question

1. Consider a speaker at some fixed position, emitting sound uniformly in all directions. You are standing at some distance d from this speaker, holding a sound-intensity measuring device. You then walk 25.0 m in a straight line towards the speaker. At this point you observe that the intensity of the sound has doubled (from the previous location). Determine the distance d. There are no echoes or reflections or interference.

2. You are standing equidistant from four identical jet engines where the sound is nearly unbearable at 123 dB. What would be the dB level where you’re standing if the pilot shut off all but one of the engines?

3. A stationary evacuation siren is blaring alongside a straight road that runs east and west. The sound wave that travels along the road can be described by D(x,t)=0.4 cos(18.5x ± 6072t). The ± here means that the wave is traveling both eastward and westward; let’s make east the positive x-direction. A traveler driving on the road, headed west, hears the siren as a steady 903.0 Hz tone.

a) What is the air temperature?

b) Is the car moving towards or way from the siren? (Explain briefly how you know.)

c) How fast is the car moving?

d) Let’s pretend that enough of the siren sound energy echoes off the car and returns to the site of the siren where a person is standing such that the person can actually hear the echo. What echo frequency would that standing person hear?

Answer #1

As the intensity of sound is inversly related to the square of distance from the sound source.

Let say at distance d intensity is I . walking 25m means now the distance from the source is( d - 25) . Writing the relationships

I = C / d^{2} ..................1

2 I = C / (d - 25)^{2} ...........2

2I = C /( d^{2} -50d + 625 )

2(
C / d^{2}) = C / d^{2} -50d + 625

2 / d^{2} = 1 / ( d^{2} - 50d + 625)

2d^{2} - 100d + 1250 = d^{2}

d^{2} - 100d + 1250 =0

d =( -100 10000 - 4(1)(1250) ) / 2

d = -14.6 m or -85.53

SO, there are two values ...Negative sign shows the motion in negative axis you can ignore it.

Please show all your work.
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