Science > Physics > 2 Short questions on speed on sound in relation to temprature - NEWBIE()!!
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Science > Physics |
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| Date: |
15 Mar 2006 03:23:53 AM |
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2 Short questions on speed on sound in relation to temprature - NEWBIE()!! |
Hi Guys,
Please note the newbie above!!!
I've start looking at physics and am a mature student and on the course
I'm doing we were given the follownig questions and answers, but no
explantation. Are the answers below correct?
Question
Given that sound speed will increase at a set rate for every 1 degree
increase in temperature. Assuming we have the following temperatures:
(is this even correct - Sarah)
0C = 332M/Sec
-10C = 323 M/Sec
+30 = 352 M/Sec
1. Based above, what is the rate of increase for 1 degree C?
3
2. Based on the previous, what is the speed of sound at -37.5C?
Answers:
1: -10 => 323 M/Sec
+30 => 352 M/Sec
=>Difference in temperature is 40 degrees C
Difference in speed is = 352 - 323 = 29 M/Sec
=> speed (29) / temperature (40) = 0.725
=> the speed of sound increases by 0.725M/Sec for every 1 degree rise
in temperature
2. Based on the previous example, calculate the speed of sound at
-37.5
degrees.
We know that -10 => 323 M/Sec
+30 is 352
-37.5C is 27.5 lower => difference of 27.5
Multiply 27.5 * 0.725 => 19.9375
As the air temperature is negative we subtract =>
323 - 19.9375 => 303.0265 M/Sec
Is the above remotely right?
For Q2, why is 19.9375 subtracted from the speed of sound at -10, is it
because in the Question that was the lowest temprature quotred?
If you know the answer, please explain in plain English. I've checked
the net but the stuff is way over my head or is there another way the
answer question 1 and 2?
Any help would be greatly appreciated.
Regards,
Sarah Hamilton.
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| User: "CWatters" |
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| Title: Re: 2 Short questions on speed on sound in relation to temprature - NEWBIE()!! |
15 Mar 2006 04:39:07 AM |
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<shamilton72@hotmail.co.uk> wrote in message
news:1142414633.430687.241450@j33g2000cwa.googlegroups.com...
Hi Guys,
Please note the newbie above!!!
I've start looking at physics and am a mature student and on the course
I'm doing we were given the follownig questions and answers, but no
explantation. Are the answers below correct?
Question
Given that sound speed will increase at a set rate for every 1 degree
increase in temperature. Assuming we have the following temperatures:
(is this even correct - Sarah)
0C = 332M/Sec
-10C = 323 M/Sec
+30 = 352 M/Sec
1. Based above, what is the rate of increase for 1 degree C?
Answers:
1: -10 => 323 M/Sec
+30 => 352 M/Sec
=>Difference in temperature is 40 degrees C
Difference in speed is = 352 - 323 = 29 M/Sec
=> speed (29) / temperature (40) = 0.725
=> the speed of sound increases by 0.725M/Sec for every 1 degree rise
in temperature
The equation for the slope is
Rate = (S2-S1)/(T2-T1)
where
S1 is the speed at T1
S2 is the speed at T2
If you calculate the speed over the whole range -10 to +30 then you get...
(352-323)/(30--10) = 0.725 M/Sec/C
2. Based on the previous, what is the speed of sound at -37.5C?
That's outside the data set of -10 to +30 so you have to assumptions that
the graph is still a straight line.
rewrite the equation to give an equation for an unknown S2...
Rate = S2/(T2-T1) - S1/(T2-T1)
Add S1/(T2-T1) to both sides
Rate + S1/(T2-T1) = S2/(T2-T1)
Multiply both sides by (T2-T1)
S2 = (Rate + S1/(T2-T1)) * (T2-T1)
Simplify
S2 = S1 + Rate*(T2-T1)
Put in the numbers
T1 = 0
S1 = 332
T2 = -37.5
and
S2 = 332 + 0.725*(-37.5-0)
= 332 - 27.188
= 304.8 M/Sec
This web site gives a figure of 307.8 which isn't that far out..
http://www.sengpielaudio.com/calculator-speedsound.htm
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