Solving Young Modulus of Metal: Density, Length, Hammer Pulse Time

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To solve for the Young Modulus of a metal rod, the speed of sound in the material is crucial, which can be calculated using the equation v = √(E/D). Given the density of the metal as 9.0 x 10^3 kg/m^3 and the time for the compression pulse to travel back and forth as 5.5 x 10^-4 s, the speed of sound can be determined. The length of the rod is 1.0 m, allowing for the calculation of Young's Modulus by rearranging the equation. The discussion highlights the importance of recognizing the relationship between speed, density, and Young's Modulus. Ultimately, applying the correct formula simplifies the problem-solving process.
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Homework Statement


A metal rod of length 1.0 m is hit with a hammer at one end. It takes 5.5x10^-4 s for the compression pulse generated to travel to the other end and reflected back to the end hit by the hammer. Find the Young Modulus of the metal.
(Given: density of the metal = 9.0x10^3 kg m^-3)


Homework Equations


E=FL/Ae
D=M/V

The Attempt at a Solution


D=M/V=M/(AxL) (L=1m)
I just don't know how to make use of the data given. Clueless. My head's going to explode!
 
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You need the equation that relates the speed of sound in a solid to its Young Modulus and density. From that you can calculate the modulus simply and directly from the other two values you are given.
Do you have this equation in your book or lecture notes?
 
Yes! Is it v=[sq. root](E/D)?

Ah, it's actually just substituting numbers into the equation... Why can't I think of this equation in the first place

Thanks a lot!
 

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