How long would it take a sound wave to travel 150m

  • Thread starter rpthomps
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  • #1
rpthomps
182
19

Homework Statement




The sound speed in air at 0 degrees Celsius is 331 m/s, and for temperatures within a few tens of degrees of 0 degrees celsius it increases at the rate 0.590 m/s for every degree celsius increase in temperature. How long would it take a sound wave to travel 150 m over a path where the temperature rises linearly from 5 degrees to 15 degrees at the other end?


Homework Equations




d= 150 m


v=331+0.59T


##T=(\frac{1}{15})x+5\\dT=\frac{1}{15}dx##


The Attempt at a Solution



##dt=\frac { dx }{ v }\\T_{ total }=\int _{ 0 }^{ 150 }{ \frac { dx }{ v } }\\=\int _{ 0 }^{ 150 }{ \frac { 15dT }{ 331+0.59T } }\\=\frac { 15 }{ 0.59 } ln(331+0.59T){ | }_{ 0 }^{ 15 }=0.67##


Back of the book says .445 s
 

Answers and Replies

  • #2
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
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Homework Statement




The sound speed in air at 0 degrees Celsius is 331 m/s, and for temperatures within a few tens of degrees of 0 degrees celsius it increases at the rate 0.590 m/s for every degree celsius increase in temperature. How long would it take a sound wave to travel 150 m over a path where the temperature rises linearly from 5 degrees to 15 degrees at the other end?


Homework Equations




d= 150 m


v=331+0.59T


##T=(\frac{1}{15})x+5\\dT=\frac{1}{15}dx##


The Attempt at a Solution



##dt=\frac { dx }{ v }\\T_{ total }=\int _{ 0 }^{ 150 }{ \frac { dx }{ v } }\\=\int _{ 0 }^{ 150 }{ \frac { 15dT }{ 331+0.59T } }\\=\frac { 15 }{ 0.59 } ln(331+0.59T){ | }_{ 0 }^{ 15 }=0.67##


Back of the book says .445 s
Is the initial temperature 0° ?
 
  • #3
rpthomps
182
19
Yup, that's it. the lower boundary should be 5 degrees. When I recalculate, I get the correct answer. Thank you sir!
 
  • #4
uknabm
1
0
how thrilling is it that using a simple formula v = d/t, you can calculate how far a thunderstorm is from you! So exciting! I love Physics!!!!!
 

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