# Reason for very low speed of sound in rubber

I just came by a table in the Class 11 Physics NCERT textbook, listing speeds of sound in different media. Vulcanised rubber has an unusually low speed of sound $$54\ \mathrm{m}/\mathrm{s}$$ as compared to the other solids, e.g $$6000\ \mathrm{m}/\mathrm{s}$$ for granite and $$3560\ \mathrm{m}/\mathrm{s}$$ for copper. This is intriguing.

Speed of sound in general is:

$$v = \sqrt{ \frac{\text{Elastic properties}}{\text{Inertial properties}}}$$

Elastic property in this case should be bulk modulus (or Youngs or shear, I am confused) which should be low to support the observation. Is this because rubber is a polymer?

I checked the internet for speed of sound in other polymers but found no satisfactory results.

I would really like to know the reason for this anomaly.

• Have you tried stretching a steel bar using your bare hands? Jan 17, 2020 at 14:06

The Young's modulus of rubber is about 4×10^6 and it's density is 1200 kg/m³ if you plug in the values in v=√(Y/μ) you get v=57.7m/s. According to me the probable cause of the anomaly should be abnormally high density of rubber due to vulcanization and abnormally low modulus of elasticity

• The density of natural rubber is about 900 kg/m$^3$. The difference between 900 and 1200 only makes 15% difference to the speed of sound which doesn't explain much of the factor of 100 difference between the speed of sound in most solids and rubber. The reason is simply that rubber has a very low modulus of elasticity compared with most solids which have Youngs modulus of order $10^{11}$ Pa, not $10^6$ Nov 30, 2018 at 20:36

Remember that sound is a vibration of kinetic energy passed from molecule to molecule.

At the particle level, a rigid material is defined by atoms and/or molecules with strong forces of attraction for each other. You must have learnt that the particles vibrate about their mean positions like springs. They quickly return to their original position.

Particles that return to their mean position quickly are ready to move again more quickly, and thus they can vibrate at higher speeds. Therefore, sound can travel faster through steel (which has high elastic properties) than it can through rubber (which has lower elastic properties). Also, rubber has a very low modulus of elasticity, unlike the other materials you mentioned.

• speed of oscillation of particle doesn't affect the speed of wave propagation. this statement of yours is wrong "and thus they can vibrate at higher speeds" Oct 27, 2020 at 14:37
• Could you cite a resource regarding this? Oct 27, 2020 at 14:47
• Khan Academy, i mean its everywhere and a well known fact, but KH can help. "Common mistakes and misconceptions Sometimes people forget wave speed isn't the same as the speed of the particles in the medium. The wave speed is how quickly the disturbance travels through a medium. The particle speed is how quickly a particle moves about its equilibrium position." Oct 27, 2020 at 14:49
• Cite some counterexamples where the wave speed is abnormally low and particle speed is high. That should convince me. Oct 27, 2020 at 14:56
• wave speed/speed of energy propagation depends on the medium where the energy/disturbance propagates, the speed of particles will only affect the frequency and not the energy propagation speed. Oct 28, 2020 at 7:27