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$\cdot$ Two train whistles, $A$ and $B,$ each have a frequency of 392 Hz. $A$ is stationary and $B$ is moving toward the right (away from $A$ ) at a speed of 35.0 $\mathrm{m} / \mathrm{s} .$ A listener is between the two whistles and is moving toward the right with a speed of15.0 $\mathrm{m} / \mathrm{s} .$ (See Figure $12.45 . )$ (a) What is the frequency from $A$as heard by the listener? (b) What is the frequency from $B$ as heard by the listener? (c) What is the beat frequency detected by the listener?

a) 375$H z$b) 370.75$H z$c) 4 $\mathrm{Hz}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

McMaster University

Lectures

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we're told we have to train with those A and B which have a frequency 392 Hertz A s stationery and he is moving toward the right away from a at a speed of 35 meters per second. A listener is between the two whistle then is moving toward this right with the speed of 15 meters per second. So we have to train Was was here. This one is stationary. This one is moving and our listeners a moving in the same direction is this one. And so we want to figure out first. What is the frequency from a as hurt by listener? Well, we have our two frequencies and the velocity of a it is get his arm zero the blast to be relative to a So again, in this case, we're gonna have a positive direction here. So we need a minus. Sign there. And so hoops not not there. We need a minus sign for the velocity of our listener which we here, minus 15 meters per second and plugging into our equation for the Doppler effect. So we have the frequency of a times this ratio of the velocity of the speed of sound and hair plus the velocity of the listener divided by the velocity of speed of sound There plus the velocity of the source. So that lost you. The listener is minus 15 meters per second. Source is not moving. We wind up with hey frequency heard by the listener of 375 hertz Now And we're also asked what is the frequency from be as heard by listeners So this time the listener positive is in the other direction. So over Go back here now In this case, this is this is for a and now positive stir action for a pee The source is moving towards listen the listener is moving towards the source So we have 15 meters per second and we can use our But now both e the listener and the source are moved So we plug in our listener speed and our source speed Multiply that by their base frequency and we wind up with 371 hurts were then asked what is the beat frequency detected by the listener? Well, that's just efforts in two frequencies from two sources. And so we get 375 hertz minus certainly for her ex for weeks, four beats per second

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