Speed of Sound: HELP!

[oncemorealoft]

I was 'helping' my daughter with her Maths homework the other night, and to try and bring the topic alive, I started to talk about Mach numbers and the speed of sound - well it seemed like a good idea at the time!

Of course, she ended up more confused by my help than if I hadn't interfered but, even worse, I confused myself.

Am I right that the speed of sound is essentially lower the higher you go? Around 707 m.p.h sea level and 600 something m.p.h at 30K+ feet? So sound travels slower at altitude than at sea level?

But why?

[alidad]

The speed of sound is PURELY a function of temperature (ie not altitude or pressure etc):

Speed of sound ~38.375 times square root of absolute temp

ie at minus 50 c (~223 deg Kelvin) at sealevel in antarctic the speed is same as minus 50 at 40000'.

Aircrft Mach no. is PURELY a function of indicated airspeed and
pressure altitude eg climbing at say 250 KIAS the Mno will progressively increase with altitude.

The 3rd variable is of course True airspeed which is another issue- hope this helps!!!;)


PS (how old is your daughter!:p

[Fg Off Max Stout]

Without wanting to be too boring or show what i've forgotten since uni the following rings a bell:

a = sqrt( gamma.R.T)

where

a= speed of sound m/s
gamma = the ratio of specific heats at constant pressure over constant volume, for air = 4/3
R= the Gas Constant for air 274 I think.
T= temperature in Kelvin (=temp in deg C + 273)

gamma and R are constant for air so the speed of sound depends only on the square root of the absolute temperature, The higher you go, the colder, so the slower the speed of sound.

If you do the maths at ISA temp 15 degC or 298K, speed of sound should me about 330m/s.

[AlphaCharlie]

Just to really throw the spanner in the works - above 11,000m (yes metres not feet) the speed of sound is a constant at 295m/s.

[mcdhu]

AC, that's because, in the standard atmosphere, the temperature is constant at -56C above the tropopause which occurs at 56,090ft. Sorry not to be in metres etc, I'm an analogue sort of a guy!
So, oncemorealoft, ballpark 'pilot' figures for the speed of sound are 660kts at sea level, 600kts at 25000ft, and 580kts at 35000ft. To convert to mph, x15% - and yes, it's all about temperature.

Hope this helps,
Cheers,
mcdhu

[KoruLounge]

Speed of sound = 38.94 x square root of absolute temperature.

Zero degree celcius = 273 degrees Kelvin. The unit scale is the same. The reason for using absolute temperature is to avoid negative values.

Speed of sound is a function of TRUE airspeed.

True Airpeed = Ground speed (In Nil wind conditions only)


To Oncemorealoft, speed of sound is ONLY related to temperature NOT altitude.

[sky9]

Lofty
Just type "speed of sound" into google and you and your daughter can be kept amused for years.
;) ;)

[Flash2001]

FOMS

Gamma for air = about 1.4, not 4/3.

[AlphaCharlie]

mcdhu,

Yes, once I had posted it I realised that it was a stupid thing to say because the constant temp is the reason why .... derrrrr...

I only quoted in metres and m/s because that was what I was taught at uni, and I can never remember the imperial equivalent!!

[error_401]

AlphaCharlie

Careful - it is only true that the speed of sound remains constant above 11'060 m (36'100 ft) up to the warming stratosphere in ISA conditions. (The assumption is an isothermy up to about 30'000 m or 100'000 ft in the ISA definition.

That means - it will shift as long as you have a temp change with altitude. In real life the Tropopause can be found at levels up to FL 500 and temp down to -63 Celsius. So you do have a change even up there. (Coffin corner greets the high flyers)

[oncemorealoft]

Thanks to everyone who took the trouble to reply. I've given my daughter some of the equations above to work out - that should keep her quiet for a while and allow me to watch Discovery Wings in peace!;)

[18greens]

KoroLounge

Is 38.94 sqrt (absolute temp) the speed of sound in Knots or MPH. I'm sure its Knots but i can't remember. The ATPLS were so long ago.

PS. I asked this question of two airline pilots about 10 years ago (when jump seat rides existed - ahhh do you remember them?) and they didn't know either. SO I DON'T FEEL EMBARRASED ASKING THE QUESTION.

PPS Once morealoft, I would be proud to have a daughter (or even a son) that was even vaguely interested in this area of physics.These interests must be fueled or else we will turn into a nation of Coronation street experts and that would never do. Save the nation, vote physics ra ra ra.