Speed of Sound in a Rod

Date: 07/05/99 at 23:00:39
From: Tyler Johnson
Subject: Sound speed

Dr. Math,

I am a home-schooler and this is a question that is on my exit exam so 
I can graduate. Neither of my parents knows where to start or how to 
explain it. Therefore if it is possible, can you explain or give the 
formula needed instead of just the answer? The problem is:

The speed of sound in an iron rod is 16,850 ft/sec, and the speed in 
air is 1100 ft/sec. If a sound originating at one end of the rod is 
heard in the rod one second before it is heard in the air, how long is 
the rod?

Thank you for looking at this.

Sincerely, 
Tyler Johnson

Date: 07/06/99 at 15:38:18
From: Doctor Fwg
Subject: Re: Sound speed

Dear Tyler,

Try the problem this way:

The distance is the same in both cases. Let that distance be D.
The time for the sound to travel through the rod is Tr.
The time for the sound to travel through the air is Ta.
The velocity of sound in the rod is 16,850 ft/sec.
The velocity of sound in air is 1100 ft/sec.

But,

     Ta = Tr + 1   (Note: Ta is longer than Tr.)
And,

     D = VrTr = VaTa = Va(Tr + 1)
so:

     VrTr = Va(Tr + 1).

Therefore:

     Vr/Va = (Tr + 1)/Tr = 16,850/1100 = 15.318
so:

     (Tr + 1)/Tr = 15.318.

Next, solve for Tr, then plug into the equation:

     D = VrTr to get D.

I hope this helps.

With best wishes,

- Doctor Fwg, The Math Forum
http://mathforum.org/dr.math/