Question
Since waves transfer energy from one point to another, one can define the power of a wave as the rate at which the wave transports energy. The intensity of a wave, in contrast, is the power relative to a certain surface. Consider a wave traveling across a surface perpendicular to the direction of propagation. The intensity I of the wave is defined as the ratio of the power P of the wave to the area A of that surface:
I=P/A
Note that the surface may be real (physical, like an eardrum or a windowpane) or mathematical. Quite frequently, we will be interested in the intensity produced by a relatively small source at a relatively large distance. If the source emits waves uniformly in all possible directions (produces spherical waves), the formula given here makes it possible to find the intensity at a distance R from the source:
i=P/4r^2
Note that, in all parts of this problem, assume that the source generates spherical waves, so that this intensity formula is applicable.
Intensity is measured in watts per square meter square. All the information presented here is pertinent to any kind of wave. In this problem, we will be focusing on sound waves.
Since waves transfer energy from one point to another, one can define the power of a wave as the rate at which the wave transports energy. The intensity of a wave, in contrast, is the power relative to a certain surface. Consider a wave traveling across a surface perpendicular to the direction of propagation. The intensity I of the wave is defined as the ratio of the power P of the wave to the area A of that surface: I=P/A Note that the surface may be real (physical, like an eardrum or a windowpane) or mathematical. Quite frequently, we will be interested in the intensity produced by a relatively small source at a relatively large distance. If the source emits waves uniformly in all possible directions (produces spherical waves), the formula given here makes it possible to find the intensity at a distance R from the source: i=P/4pi r^2 Note that, in all parts of this problem, assume that the source generates spherical waves, so that this intensity formula is applicable. Intensity is measured in watts per square meter square. All the information presented here is pertinent to any kind of wave. In this problem, we will be focusing on sound waves. A popular car stereo has four speakers, each rated at 60 m from each of the two rear speakers. m from each of the two front speakers and 1.5 W speakers as heard by the driver. Assume that the driver is located 1.0 I of the sound waves produced by four 60- m . C) Find the intensity W speaker at a distance of 1.5 I of the sound waves produced by one 60- m . B) Find the intensity W speaker at a distance of 1.0 I of the sound waves produced by one 60- W . In answering the following questions, assume that the speakers produce sound at their maximum power. A) Find the intensity
Explanation / Answer
a) I1=P/4pir^2=60/4pi=4.8(W/m2). b) I2=P/4pi1.5^2=2.12(W/m2). c) we have I_total = 2*I1+2*I2 =2*4.8+2*2.12=13.8(W/m2)