Time on watch dependent on air temperature?

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Homework Help Overview

The problem involves calculating the time delay of a watch set by the sound of a factory whistle located 3 miles away, considering the speed of sound in air at a temperature of 20 degrees Celsius. Participants are exploring the relationship between sound speed, distance, and time.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the speed of sound at 20 degrees Celsius and its implications for calculating time. There are attempts to convert distance into feet and meters, and to apply the formula for time based on velocity and distance. Some participants express uncertainty about how to structure their calculations.

Discussion Status

There is ongoing exploration of the problem with participants sharing calculations and questioning their results. Some guidance has been offered regarding the relationship between distance, speed, and time, but no consensus has been reached on the final answer.

Contextual Notes

Participants are working under the constraints of the problem's parameters, including the temperature and the distance to the factory. There is also a mention of the common experience of thunder and lightning as a conceptual reference point for understanding sound delay.

kriegera
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Homework Statement


Can anyone give me a hand on how to start this? I would attempt a solution but I've tried over and over and can't seem to get anywhere.

A man sets his watch at noon by the sound of a factory whistle 3 miles away. If the temperature of the air is 20-degrees C, how many seconds slow will his watch be by the time at the factory?


Homework Equations





The Attempt at a Solution

 
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How fast does sound travel through air at 20C?
 
DaveC426913 said:
How fast does sound travel through air at 20C?


Still a little lost here:

In general, at 68 F (20 C) sound travels at 1130 ft/sec (344.4 m/sec.)
3 miles = 15 840 feet
3 miles = 4 828.032 meters

but not sure how to put it together in equation format?
 
kriegera said:
Still a little lost here:

In general, at 68 F (20 C) sound travels at 1130 ft/sec (344.4 m/sec.)
3 miles = 15 840 feet
3 miles = 4 828.032 meters

but not sure how to put it together in equation format?

Really?

You've got a velocity and a distance; you're being asked to solve for time.

You say you're tried over and over. Show your attempts.
 
DaveC426913 said:
Really?

You've got a velocity and a distance; you're being asked to solve for time.

You say you're tried over and over. Show your attempts.

T=V/D =
T=15840 ft/ 1130ft/s = 14.018 seconds.
 
kriegera said:
T=V/D =
T=15840 ft/ 1130ft/s = 14.018 seconds.

Does that sound about right? What does your intuition tell you? Think of thunder & lightning.
 
DaveC426913 said:
Does that sound about right? What does your intuition tell you? Think of thunder & lightning.

I did find something that used c = d / Δ t - where c was speed of sound so
Δ t = d / c = 15,840/344.4 = 46 seconds but that seems too long a delay for three miles no?

As far as thunder and lightning, lightning strikes first b/c it travels faster in air than sound. The speed of a sound wave in air depends upon the properties of the air, namely the temperature and the pressure so it makes sense for
Time=distance/speed =
Time=15,840 ft/1130 ft/sec.
14.018 sec

but I'm still second-guessing it.
 

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