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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

A jet plane passes over you at a height of 5000鈥尘and a speed of Mach 1.5.

(a) Find the Mach cone angle (the sound speed is 331鈥尘/s).

(b) How long after the jet passes directly overhead does the shock wave reach you?

In figure, sound wavesand, both of wavelength位, are initially in phase and traveling rightwards , as indicated by the two rays. Ways Ais reflected from four surfaces but ends up traveling in its original direction. Waveends in that direction after reflection from two surfaces. Let distance Lin the figure expressed as a multipleq鈥�位:L=辩位.What are the(a)Smallest (b)Second smallest value of qthat put Aand Bexactly out of phase with each other after the reflection ?

In Fig. 17-46, sound of wavelength 0.850鈥尘is emitted isotropically by point source S. Sound ray 1 extends directly to detector D, at distance L=10.0鈥尘. Sound ray 2 extends to Dvia a reflection (effectively, a 鈥渂ouncing鈥�) of the sound at a flat surface. That reflection occurs on a perpendicular bisector to the SDline,at distance dfrom the line. Assume that the reflection shifts the sound wave by0.500位. For what least value of d(other than zero) do the direct sound and the reflected sound arrive at D(a) exactly out of phase and (b) exactly in phase?

Question: Figure 17-30 shows a stretched string of lengthand pipes a,b, c, and dof lengthsL, 2L, L/2, andL/2, respectively. The string鈥檚 tension is adjusted until the speed of waves on the string equals the speed of sound waves in the air.Thefundamental mode of oscillationis then set up on the string. In which pipe will the sound produced by the string cause resonance, and what oscillation mode willthat sound set up?

Question: In Fig. 17-27, pipe Ais made to oscillate in its third harmonicby a small internal sound source. Sound emitted at the right endhappens to resonate four nearby pipes, each with only one openend (they are notdrawn to scale). Pipe Boscillates in its lowestharmonic, pipe Cin its second lowest harmonic, pipe Din itsthird lowest harmonic, and pipe Ein its fourth lowest harmonic.Without computation, rank all five pipes according to theirlength, greatest first. (Hint:Draw the standing waves to scale andthen draw the pipes to scale.)
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