Question

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.

Answer 1

Answer:

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