Time on watch dependent on air temperature?

[kriegera]

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

 

[DaveC426913]

How fast does sound travel through air at 20C?

 

[kriegera]

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?

 

[DaveC426913]

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.

 

[kriegera]

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.

 

[DaveC426913]

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.

 

[kriegera]

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.