Speed of Sound in Perfection

Classical Mechanics Level 3

The speed of sound in a perfectly rigid rod is

5000

m/s Less than

332

m/s Zero Infinite

332

m/s

3 solutions

Nicole Tay
Jan 10, 2016

The velocity of longitudinal waves in a solid is given by $\sqrt { \frac { Y }{ \rho } }$ where Y is the Young's Modulus and $\rho$ is the density of the solid. Young's Modulus is the ratio of stress to strain. In a perfectly rigid body, strain=0 because the body will not change in length. Hence Young's Modulus is infinite, making the velocity of sound also infinite.

Nice! I thought of it this way : When we try to define "perfectly rigid rod" then we infer that the inter-molecular distance between the atoms of the rod is infinitely small. So the time taken for sound energy to move from atom to atom is infinitely small as well. Hence , the speed of sound must be infinite.

Nihar Mahajan - 5 years, 5 months ago

You're making too many assumptions. You can easily solve this without any of that knowledge.

Jake Lai - 5 years, 4 months ago

A simpler way to think about it would be that no compression/rarefaction would occur, so sound would immediately propagate through the rod.

Jake Lai - 5 years, 4 months ago

Wouldn't you need to take relativistic effects into account here? I am pretty sure 'perfectly rigid' means that the speed of sound is equal to the speed of light. Sort of like how the speed at which the rest of the material moves (catches us) when you move the rod from one end is equal to the speed of sound in that material, so the speed of sound is sort of like a measure of the propagation of causality within a medium and the universal maximum speed at which causality can propagate is the speed of light.

Tristan Goodman - 1 year, 12 months ago

Does that make the waves break light speed though? Or is it that perfectly rigid bodies are impossible?

Aloysius Ng - 5 years, 4 months ago

Perfectly rigid bodies are impossible.

Jake Lai - 5 years, 4 months ago

Aditya Kumar
Jan 29, 2016

Alternate Solution:

We know sound is produced due to vibration. In a perfectly rigid body all the molecules are tightly bound to each other. There is no space between any molecule. So if there is disturbance in any one molecule, it will be felt in other molecules without any time lag (that instant itself). Hence time taken for that disturbance is 0. Therefore speed =distance/0=infinity.

Rishabh Jain
Dec 27, 2015

Evident from the title. You should have kept one or two dummy options like 3c,3c/2 etc...

Speed of Sound in Perfection

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