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Lesson 4: Sound

# Mach numbers

We can measure speeds relative to the speed of sound. Created by Sal Khan.

## Want to join the conversation?

• The Wikipedia article referenced below shows a cool picture of a vapor vortex forming around a military aircraft as it exceeds Mach 1. By what mechanism does this vapor cloud form?
http://en.wikipedia.org/wiki/File:FA-18_Hornet_breaking_sound_barrier_%287_July_1999%29.jpg
• When water has enough warmth in a low enough pressure environment, liquid water evaporates (clear colorless gas, invisible). When evaporated water is compressed, some may condense to form liquid water (droplets have light bouncing all around them and inside them, so they seem white and cloudy). As the aircraft reaches Mach 1, it's sound adds such that several moments of sound are in the same location. This enormous push compresses the air in front of the craft enough to squish water vapor into droplets, a cloud.
• doesn't the speed of sound get faster when it gets colder because the air is denser?
• Sound is a compression wave. The speed it travels through something is dependent on how quickly the energy can pass between adjacent atoms/molecules of what the sound is traveling through.

When a gas is colder the molecules are closer but they are also moving slower. Since temperature is a measurement of average kinetic energy it is directly related to the particles velocity. Temperature and volume are directly related so when the temperature doubles the particle velocity doubles and so does the volume but the average distance increases by 1.25.

It takes less time to travel the 1.25 times the distance at 2 times the speed allowing for the sound to propagate faster at higher temperatures.
• why does a sonic boom occur when an object (plane) goes faster than sound ?
• good question;

I will try explaining without diagram :-)

Sound is produced by a series of pushes and pulls by a vibrating body (engine, say). so now Imagine part of the plane that is producing noise.
When the plane is moving slowly, the sounds wave moves away from the plane at a speed that is faster than the plane. Imagine the waves moving away from the plane in all directions.

Now imagine that part of the sound that is moving away from the plane in the same direction as the plane is moving; forward.
OK so far ?? :-)

We might say that the sound wave is trying to 'escape' from the plane but when the plane starts to move really fast, ie the speed of sound, it is able to catch up with the sound so it can not 'escape'.
This means the vibrating part of the plane is now pushing on the same part of the sound wave; the vibration is feeding energy into the same part of the wave and the sound can not escape. so the energy builds up.
Whilst the plane is moving at the speed of sound, this build up will continue and the bulge of energy spreads out and anyone in the way (ie when it reaches the ground) will feel a very big change in pressure. this is the boom.

When a plane is accelerating, it will only be travelling at the speed of sound for a short time so the boom is quite short-lived

Hope that helps
• Consider a body moving silently (not a source of sound) attaining speed of sound ,so does it needs to break the sound barrier ?,does it produce sonic boom
• Yes, the sound barrier doesn't really have anything to do with the sound an object makes, it has to do with the fact that the object has to push air molecules out of the way as it moves. This creates a pressure wave along the front surface of the object, because air molecules can only get out of the way so fast. The pressure builds and builds as you get closer to the speed of sound.
• Sal you said that as temprature decreases speed of sound also decreases, but as temprature decreases air gets denser. So, shouldn't the speed of sound increase.
• You are correct about the increase in density of air with decrease in temperature.
However,
In the formula,
speed of sound(v) = square root of (B (known as the bulk's modulus) / density of the medium)
We see that density of medium is in the denominator.
That's why the speed of sound is inversely proportional to the square root of the density of the medium.
So,
Speed of sound decreases with the increase in density(or temperature), and does not increase.
(1 vote)
• I don't understand why the speed of sound decreases as the temperature decreases. The compressions of the particles in the medium should have less of a problem to propagate the energy if the medium is more dense (the wave sound should, if it is as Sal said, propagate better in a very low-densty medium, and in an extreme case, in vacuum where there is no density at all)... As a matter of fact, the human ears are separated in such way, that they can distinguish the direction from which the sound wave is coming from. When you are underwater it is if not impossible, very difficult to know what direction a sound wave is coming from.
• With respect to the speed of sound propagation comparing a gas with a liquid or even a solid based solely on density is not a fair comparison. There is more difference between liquids and gasses than just density. The inter molecular forces between molecules/atoms in a liquid or solid are much greater to the transmission of energy through a liquid or solid is much faster than in a gas. These molecular forces are more important for sound transmission in solids take a look at lead vs glass, lead is much denser but doesn't really transmit sound well where as glass does.

But back to looking at a gas only. The factors that effect the rate of sound propagation through a gas comes down to average distance between molecules/atoms and their average velocity. When the temperature of a gas decreases the number of particles in a volume increase and the particle velocities decrease. Based on the ideal gas law the rate of change of particles for a change in temperature is proportional to -1/dt^2 where as the change in velocity is 1/sqrt(dt) where dt is the change in temperature. You can see that the velocity change is grater than the change in number of particles. So even though the density does increase the velocity decreases more so the sound will not propagate as fast in cold air despite the increase in density.
• What would happen if an aircraft was moving faster than the speed of sound while blasting a song on the radio? Would somebody on the ground hear the song backwards? Hopefully I'm explaining this well enough.
• i guess the listeners would not listen the song at all. as it's flying away from them than the speed of the song can travel to reach them

a similar example might be the lights far from us than the speed of expansion of the universe, we can never get the lights for the same reason above
(1 vote)
• why does sound travel as transverse wave in solids??
• Sound does not convert to a transverse wave to travel through a solid.
But solids can carry transverse waves that gases and liquids cannot. This is simply because the molecules of the solid are bound together, so they can pull on each other, whereas gas and liquid molecules can't do that.
So you can have different sorts of "sound" waves in a solid, although its not clear that you would want to call them sound waves since you don't have any way to stick your ear inside a solid and hear those sounds. I think it is clearer to refer to those waves just as vibrations.