Multiple-Concept Example 11 provides a model for solving...

Multiple-Concept Example 11 provides a model for solving this type of problem. A wireless transmitting microphone is mounted on a small platform that can roll down an incline, directly away from a loudspeaker that is mounted at the top of the incline. The loudspeaker broadcasts a tone that has a fixed frequency of $1.000 \times 10^{4} \mathrm{~Hz}$, and the speed of sound is $343 \mathrm{~m} / \mathrm{s}$. At a time of $1.5 \mathrm{~s}$ following the release of the platform, the microphone detects a frequency of $9939 \mathrm{~Hz}$. At a time of $3.5 \mathrm{~s}$ following the release of the platform, the microphone detects a frequency of $9857 \mathrm{~Hz}$. What is the acceleration (assumed constant) of the platform?

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Key Concepts

Doppler Effect

The Doppler effect explains how the observed frequency of a wave changes when there is relative motion between the source and the observer. In this context, the change in the frequency detected by the microphone compared to the transmitted frequency allows for the calculation of the microphone's speed relative to the source.

Constant Acceleration Kinematics

This concept involves using kinematic equations that describe the motion of an object under uniform acceleration. It provides the framework to determine the acceleration of the platform by relating the time intervals to changes in velocity as measured indirectly through the Doppler effect.

Relative Motion Analysis

Relative motion analysis is used to interpret how velocities measured by one observer, who is in motion, differ from those of a stationary source. It is crucial for linking the observed frequency shifts to the actual speed of the moving platform, and ultimately to its acceleration when combined with constant acceleration principles.

Transcript

00:01 In this problem, we are going to calculate exploration off the platform where microphones mounted.

00:06 That is a in order to kill clearly sex operation.

00:11 We need to find the speed off the blood former two different points.

00:16 So for this purpose, we ride the equation.

00:20 If my articles to be minus weepy one divided by v in tow efforts here, if not, is the frequency received by the observer with the speed of sound.

00:31 V p one is the speed of platform at time t equals toe won t one and effort with the pregnancy off the stationary source no falling this equation for veep iman you can write we p one equals two into one minus.

00:49 If not one the worried barefaced into be please get up.

00:55 That is, if not one in the first requirement.

00:59 No, we call this equation as a wooden one.

01:03 Similarly, the street off the platform a time t d equals 22.

01:08 He is the internet.

01:11 We p two equals two into one minus if not two divided by a fence in tow.

01:16 We we call this equation too here the self not to is the frequency received by the microphone at time t because to me, too mobile in setting the world is in tow.

01:29 First question we will get we p one equals two into one.

01:35 Minus 9939 hertz to 81.0 multiple opportunities...

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