document.write( "Question 1181384: The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you to sound lower pitched, like observed in listening to the car horn in the video.\r
\n" ); document.write( "\n" ); document.write( "The equation for this is f=(c/c+v)f0 , where
\n" ); document.write( "f is the observed frequency (pitch) of the sound, in Hertz
\n" ); document.write( "c is the speed of sound, about 761 miles per hour,
\n" ); document.write( "v is the speed of the sound source, in this case the car, in miles per hour
\n" ); document.write( "f0 is the frequency of the sound when stationary\r
\n" ); document.write( "\n" ); document.write( "Using a spectrum analyzer, we could determine the observed frequency when the car was driving away was 238 Hz and the stationary frequency was 255 Hz.\r
\n" ); document.write( "\n" ); document.write( "Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place. \n" ); document.write( "

Algebra.Com's Answer #811278 by ikleyn(52915) $\"\"$ $\"About$

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\n" ); document.write( "The Doppler effect causes a sound moving towards you to sound higher pitched and a sound moving away from you
\n" ); document.write( "to sound lower pitched, like observed in listening to the car horn in the video.
\n" ); document.write( "The equation for this is f=(c/c+v)f0 , where
\n" ); document.write( "f is the observed frequency (pitch) of the sound, in Hertz
\n" ); document.write( "c is the speed of sound, about 761 miles per hour,
\n" ); document.write( "v is the speed of the sound source, in this case the car, in miles per hour
\n" ); document.write( "f0 is the frequency of the sound when stationary
\n" ); document.write( "Using a spectrum analyzer, we could determine the observed frequency when the car was driving away
\n" ); document.write( "was 238 Hz and the stationary frequency was 255 Hz.
\n" ); document.write( "Use this information and the equation to estimate the speed of the car in miles/hour, to 1 decimal place.
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\n" ); document.write( "\n" ); document.write( "As formulated, this text may PERPLEX a student, who reads this description first time in his (or her) life.\r
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\n" ); document.write( "\n" ); document.write( "For clarity, the formula must be deciphered in two forms \r
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\n" ); document.write( "\n" ); document.write( "             - for approaching source of sound     f = $\"%28c%2F%28c-v%29%29f%5B0%5D\"$ ,          (1)\r
\n" ); document.write( "\n" ); document.write( "         and \r
\n" ); document.write( "\n" ); document.write( "             - for receding       source of sound     f = $\"%28c%2F%28c%2Bv%29%29f%5B0%5D\"$ ,         (2)\r
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\n" ); document.write( "\n" ); document.write( "where \"v\" is the positive MAGNITUDE of the relative velocity.\r
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document.write( "With the numerical data given at the end of the post, we have case (2) (the car driving away).\r\n" );
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document.write( "So, all we need to do is to substitute the given frequencies into equation (2)\r\n" );
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document.write( "    238 = .\r\n" );
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document.write( "To solve it, cross multiply, simplify and find v\r\n" );
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document.write( "    238(761 + v) = 255*761\r\n" );
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document.write( "    761 + v =  = 815.4 mph\r\n" );
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document.write( "          v                       = 815.4 - 761 = 54.4 mph.\r\n" );
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document.write( "ANSWER.  The speed of the car is 54.4 miles per hour.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and carefully explained.\r
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