Baseball scouts often use a radar gun to measure the speed of a pitch. One parti

Question

Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz ?f= Hz ?f= Hz Baseball scouts often use a radar gun to measure the speed of a pitch. One particular model of radar gun emits a microwave signal at a frequency of 10.525 GHz. Part A What will be the increase in frequency if these waves are reflected from a 60.0mi/h fastball headed straight toward the gun? (Note: 1 mi/h= 0.447 m/s ) ?f= Hz

Explanation / Answer

the fastball will see a frequency of

f1 = sqrt( (1 + beta)/(1 - beta) ) f0

this will then be the source that goes back to gun

f2 = sqrt( (1 + beta)/( 1 - beta) ) f1 = ( 1 + beta)/(1 - beta) f0

f2 - f0 = (1 + beta)/(1 - beta) f0 - f0 = ( 1 + beta - (1 - beta))/(1 - beta) f0 = 2 beta f0/(1 - beta) = 2*60*(0.447/3E8)*10.525E9/(1-60*(0.447/3E8))=1882 Hz

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