Two metal rods are made of different elements. The interatomic spring stiffness of element A is 7 times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is 7 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.

Question

Physics

Boston Golden

21 December, 00:52

Two metal rods are made of different elements. The interatomic spring stiffness of element A is 7 times larger than the interatomic spring stiffness for element B. The mass of an atom of element A is 7 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.

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Answers (1)

Know the Answer?

Haleigh Gordon · Answer 1

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

Explanation:

Applying Hooke's law,

F = - kx

Where,

F = force

k = spring stiffness

x = length

Element A

F/7k = x

Since, mass = F/A

Ma = 7Mb

Therefore,

7Mb/A*7kb = x

Mb/A*k = x

Element B

F/k = x

Since, mass = F/A

Mb = Mb

Therefore,

Mb/A*kb = x

Ratio of mass of element A and element B

Mb/A*kb : Mb/A*kb

1 : 1