The speed of sound depends on the density of the medium in which it is travelling and increases when the density increases. For example, in solids sound travels faster than in liquid and even faster than in gas, and the density is highest in solids, lower in liquids and lowest in gas.
So iron has a density of about 7,800 kg/m$^3$, while mercury has 13,600 kg/m$^3$, but the speed of sound is 1,450 m/s in mercury and 5,130 m/s in iron, so mercury has a higher density, but sound travels slower in it. Why is this?
Answer
The speed of sound in a liquid is given by:
$$ v = \sqrt{\frac{K}{\rho}} $$
where $K$ is the bulk modulus and $\rho$ is the density. The bulk modulus of mercury is $2.85 \times 10^{10}$ Pa and the density is $13534$ kg/m$^3$, so the equation gives $v = 1451$ m/sec.
The speed of sound in solids is given by:
$$ v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}} $$
where K and G are the bulk modulus and shear modulus respectively. The bulk modulus of iron is $1.7 \times 10^{11}$ Pa, the shear modulus is $8.2 \times 10^{10}$ Pa and the density is $7874$ kg/m$^3$, so the equation gives $v = 5956$ m/sec.
You give a slightly different figure for the speed of sound in iron, but the speed does depend on the shape and the figure you give, $5130$ m/sec, is the speed in a long thin rod. There are more details in the Wikipedia article I've linked.
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