Amount of time taken for truck over 5.0km

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SUMMARY

The discussion focuses on calculating the time it takes for a fire truck to travel 5.0 km based on the Doppler effect observed in sound frequencies. The approaching frequency is noted at 460 Hz, while the receding frequency is 410 Hz. The user attempts to derive the truck's velocity using the formulas for apparent frequency, resulting in two equations: 460 = f(340)/(340+v) and 410 = f(340)/(340-v). By manipulating these equations, the user can isolate the velocity and subsequently calculate the time using the formula t = Δx/v.

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  • Doppler effect in sound waves
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  • Knowledge of the formula for time calculation (t = Δx/v)
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Homework Statement


Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 460 Hz; as the truck recedes, you hear a tone of 410 Hz. How much time will it take for the truck to get from your position to the fire 5.0km away, assuming it maintains a constant speed.


Homework Equations


t = Δx/v



The Attempt at a Solution


I'm trying to find the velocity of the truck first so I have 460 = f(340)/(340+v) for the approaching tone, and a receding tone represented by 410 = f(340)/(340-v) and I'm not exactly sure what to do next. Thanks for the help.
 
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When the source approaches, the apparent frequency increases. So in the formula for apparent frequency,
denominator should be 340 -v. Write the two formulae and divide to cancel f. Then simplify to get the velocity.
 

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