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Chapter 17: Q99P (page 512)

You are standing at a distance D from an isotropic point source of sound. You walk50.0m toward the source and observe that the intensity of the sound has doubled. Calculate the distanceD.

Short Answer

Expert verified

The distance Dis 171鈥尘.

Step by step solution

01

The given data

The value of the distance is 171鈥尘.

02

Determine the concept of the intensity

Using the proportionality between the intensity of sound and distance, we can find the distance D.

Formula:

The intensity of the sound wave is inversely proportional to the square of distance or separation, I伪1r2 (i)

03

Calculate the distance

As given above we can say that

The distance betweenandis. Initially, the observer is at point D and then moves towardsthesource by 50.0m to reach at point d. At point d,the intensity of sound gets doubled.

So, we can write, the intensity and distance relation using equation (i) as:

Ir=dIr=D鈭�d=(D鈭�d)2D2=12

Solve by the quadratic formula:

D鈭�dD=12D=d1鈭�12D=170.77D~171鈥尘

Hence, the value of distance, D is 171鈥尘.

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Most popular questions from this chapter

Question: A source S and a detector D of radio waves are a distancedapart on level ground (Fig. 17-52). Radio waves of wavelength 位reach D either along a straight path or by reflecting (bouncing) from a certain layer in the atmosphere. When the layer is at heightH, the two waves reaching D are exactly in phase. If the layer graduallyrises, the phase difference between the two waves gradually shifts, until they are exactly out of phase when the layer is at height H +h. Express 位in terms of d, h, and H.

(a) If two sound waves, one in air and one in (fresh) water, are equal in intensity and angular frequency, what is the ratio of the pressure amplitude of the wave in water to that of the wave in air? Assume the water and the air are at 20掳C. (See Table 14-1.)

(b) If the pressure amplitudes are equal instead, what is the ratio of the intensities of the waves?

Question: Two loud speakers are located 3.35 mapart on an outdoor stage. A listener is18.3m from one andfrom the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range 20Hz to 20 KHz. (a) What is the lowest frequency fmin1that gives minimum signal (destructive interference) at the listener鈥檚 location? By what number must fmin1be multiplied to get(b)The second lowest frequencyfmin2that gives minimum signal and(c)The third lowest frequencyfmin3that gives minimum signal ?(d)What is the lowest frequencyfmin1that gives maximum signal (constructive interference) at the listener鈥檚 location ? By what number mustfmin1be multiplied to get(e) the second lowest frequencyfmin2that gives maximum signal and(f) the third lowest frequencyfmin3that gives maximum signal?

In Fig. 17-45, sound wavesAandB, both of wavelength位, are initially in phase and traveling rightward, as indicated by the two rays. Wave Ais reflected from four surfaces but ends up traveling in its original direction. What multiple of wavelength位is the smallest value of distanceLin the figure that puts Aand Bexactly out of phase with each other after the reflections?

In figure, two speakers separated by the distanced1=2.00mare in phase. Assume the amplitudes of the sound waves from the speakers are approximately the same at the listener鈥檚 ear at distanced2=3.75mdirectly in front of one speaker. Consider the full audible range for normal hearing, 20Hz to20鈥�KHz.

(a)What is the lowest frequency fmax1
that gives minimum signal (destructive interference) at the listener鈥檚 ear? By what number mustfmax1be multiplied to get

(b) The second lowest frequencyfmin2that gives minimum signal and

(c) The third lowest frequencyfmin3 that gives minimum signal ?

(d) What is the lowest frequency fmax1that gives maximum signal (constructive interference) at the listener鈥檚 ear ? By what number mustfmax1be multiplied to get

(e) the second lowest frequencyfmax2that gives maximum signal and

(f) the third lowest frequency fmin3that gives maximum signal?
See all solutions

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