Time on watch dependent on air temperature?

In summary: 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?
  • #1
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0

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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  • #2
How fast does sound travel through air at 20C?
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 

1. How does air temperature affect the time on a watch?

Air temperature can affect the time on a watch in two ways. First, extreme temperatures can cause the battery to drain faster, resulting in a loss of time accuracy. Second, extreme temperatures can cause the internal mechanics of the watch to expand or contract, which can also affect its accuracy.

2. Can a change in air temperature affect the time on a watch instantly?

Yes, a change in air temperature can have an instant effect on the time displayed on a watch. This is especially true for digital watches that rely on battery power, as extreme temperatures can drain the battery quickly. For mechanical watches, the effects may be more gradual, but still noticeable.

3. Is there a specific temperature range that is ideal for maintaining accurate time on a watch?

The ideal temperature range for maintaining accurate time on a watch is between 41°F (5°C) and 95°F (35°C). Outside of this range, the watch may experience inaccuracies due to the effects of extreme temperatures on its internal components.

4. How can I keep my watch accurate in extreme temperatures?

To keep your watch accurate in extreme temperatures, it is important to avoid exposing it to temperature extremes. This can be done by removing the watch when entering environments with extreme temperatures, such as a sauna or freezer. Additionally, keeping the watch in a cool, dry place when not wearing it can also help maintain its accuracy.

5. Are there any specific types of watches that are more resistant to temperature changes?

Certain types of watches, such as dive watches, are designed to withstand extreme temperatures and pressure changes. These watches are typically sealed and have more robust internal mechanics, making them more resistant to the effects of temperature changes. However, it is still important to avoid exposing any watch to extreme temperatures to ensure accurate timekeeping.

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