Question

Two rods are both made of pure titanium. The diameter of rod A is twice the diameter of rod B, but the lengths of the rods are equal. You tap on one end of each rod with a hammer and measure how long it takes the disturbance to travel to the other end of the rod. In which rod did it take longer? (a) Rod A. (b) Rod B. (c) The times were equal

Short answer

The disturbance travels to the other end of the rod.

Option c) the times were equal.

Step-by-step solution

Identification of given data

The diameter of rod A$d_A$ , the diameter of rod B$d_B$ , and the length of rods A and B are the same, $L{d}_A=2d_B$

Speed of soundStep 2: Speed of sound

Expression for speed of sound in a solid object is,

$v=\sqrt{\frac{k_{sj}}{m_a}}{d}_a$

Where$v$ is the speed of sound,$m_a$ is the mass of an atom,$k_{sj}$ is the interatomic bond stiffness of the metal, and$d_a$ is the diameter of the atom.

As both rods have the same material, so the mass of the atom, stiffness of the metal, and diameter of the atom is the same. So, the speed of sound on both rods is the same.

The time of the travel is,

$t=\frac{L}{v}$

As the length of rods is equal, the speed of sound on both rods is the same. So that time travel is also the same on both the rod. So the correct option is C.