Archibald, an aging geezer, is out bicycling one fine afternoon, reliving his glorious youth and oblivious to the world around him. As he approaches a busy intersection, a police officer directing traffic blows his whistle to get Archie’s attention so he’ll slow down and stop. But Archie doesn’t stop; he just speeds right through the intersection as if the traffic cop wasn’t even there. The cop radios one of his colleagues and gets her to stop the old geezer. She gives him a traffic citation for failing to heed the command of a police officer directing traffic. When the case gets to traffic court, Archie explains to the judge that he didn’t hear the officer’s whistle because he is going deaf and cannot hear frequencies above 3000 Hz. The traffic cop informs the judge that his standard issue police whistle emits a frequency of 2100 Hz and he has a certificate to prove it. Thinking quickly (at least for an old geezer) Archie says that it may be true that the police whistle emits a sound of 2100 Hz, but since he was riding towards the officer, the sound from the officer’s whistle was Doppler shifted above the highest frequency Archie can hear. Is Archie’s explanation reasonable? How fast would Archie have to be bicycling in order for his explanation to be valid? (Note that 1 m/s is equal to 2.22 mph.)
Archibald, an aging geezer, is out bicycling one fine afternoon, reliving his glorious youth and oblivious to the world around him. As he approaches a busy intersection, a police officer directing traffic blows his whistle to get Archie’s attention so he’ll slow down and stop. But Archie doesn’t stop; he just speeds right through the intersection as if the traffic cop wasn’t even there. The cop radios one of his colleagues and gets her to stop the old geezer. She gives him a traffic citation for failing to heed the command of a police officer directing traffic. When the case gets to traffic court, Archie explains to the judge that he didn’t hear the officer’s whistle because he is going deaf and cannot hear frequencies above 3000 Hz. The traffic cop informs the judge that his standard issue police whistle emits a frequency of 2100 Hz and he has a certificate to prove it. Thinking quickly (at least for an old geezer) Archie says that it may be true that the police whistle emits a sound of 2100 Hz, but since he was riding towards the officer, the sound from the officer’s whistle was Doppler shifted above the highest frequency Archie can hear.
Is Archie’s explanation reasonable? How fast would Archie have to be bicycling in order for his explanation to be valid? (Note that 1 m/s is equal to 2.22 mph.)
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