Amount of time taken for truck over 5.0km

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In summary, the problem involves finding the time it takes for a fire truck to travel 5.0km while maintaining a constant speed, based on the change in frequency of its siren as it approaches and recedes from a stationary observer. The relevant formula is t = Δx/v and the approach and receding tones can be represented by the equations 460 = f(340)/(340+v) and 410 = f(340)/(340-v), respectively. To find the velocity, these equations can be divided and simplified.
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icesalmon
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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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  • #2
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.
 

FAQ: Amount of time taken for truck over 5.0km

1. What is the average amount of time it takes for a truck to travel 5.0km?

The average amount of time it takes for a truck to travel 5.0km can vary depending on various factors such as the weight of the truck, the condition of the road, and the speed limit. However, on average, a truck can travel 5.0km in 5-7 minutes.

2. How does the weight of the truck affect the amount of time it takes to travel 5.0km?

The weight of a truck can significantly affect the amount of time it takes to travel 5.0km. The heavier the truck, the slower it will travel, and thus, it will take more time to cover the distance.

3. Can the condition of the road impact the amount of time it takes for a truck to travel 5.0km?

Yes, the condition of the road can have a significant impact on the amount of time it takes for a truck to travel 5.0km. A well-maintained road with no obstacles or traffic will allow the truck to travel faster, while a road with potholes or heavy traffic will slow down the truck and increase the travel time.

4. Is there a maximum speed limit for trucks when traveling 5.0km?

The speed limit for trucks when traveling 5.0km can vary depending on the country or state. However, most places have a speed limit of 50-60 km/h for trucks on highways, which would take approximately 5-7 minutes to travel 5.0km.

5. How can the amount of time taken for a truck to travel 5.0km affect transportation and logistics?

The amount of time it takes for a truck to travel 5.0km can greatly impact transportation and logistics. A longer travel time can lead to delays in delivering goods, which can affect the supply chain and customer satisfaction. Therefore, it is crucial for trucking companies to optimize their routes and ensure timely delivery to avoid any disruptions in the supply chain.

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