Two metal rods are made of different elements. The interatomic spring stiffness

Question

Two metal rods are made of different elements. The interatomic spring stiffness of element A is six times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is six times greater than the mass of an atom of element B. The atomic diameters are approximately the same for A and B. What is the ratio of the speed of sound in rod A to the speed of sound in rod B?

A) The ratio of the speed of sound in rod A to the speed of sound in rod B is 0.5.

B) The ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

C) The ratio of the speed of sound in rod A to the speed of sound in rod B is 2.

D) The ratio of the speed of sound in rod A to the speed of sound in rod B is 6.

Explanation / Answer

f = 1/(2*pi)*Sqrt(k/m).

As the mass (m) increases, the frequency will decrease, which implies longer oscillation period, and the wave will propagate slower. Not mass is 6 times and so is the pring stiffness

Hence they cancel out.

B) The ratio of the speed of sound in rod A to the speed of sound in rod B is 1.

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