# Supersonic wave and distance calculation

• 2tts
In summary, when calculating the distance from a stationary visible object using the speed of sound when dealing with a supersonic blast wave, it is important to consider the duration of the supersonic blast wave and the standard speed of sound (adjusted for temperature). Additionally, variables such as temperature and elevation can also impact the velocity reduction over time and distance. When determining the difference between when you see something and when you hear it, it is important to keep in mind that the supersonic blast wave may only last for a few milliseconds. However, even at a great distance, the sound may still appear to be a sonic boom or supersonic, which can be attributed to factors such as the temperature and the distance itself. Similarly, when observing a volcano eruption,
2tts
To calculate the distance from a stationary visible object using the speed of sound when dealing with a supersonic blast wave from that object, how would one proceed?
Is the standard 340m/s good enough reference?
How is the velocity reduction over time and distance?

Does all the variables (temperature, elevation and such) have a notable impact on velocity reduction?
For these examples let's say sea level at 20C.

Example 1:
Looking at a large amount of high exploive, TNT, going off from far away, say 5km. How to calculate distance?

Example 2:
This is what triggerd me into reserching this.
A volcano eruption caused a shock wave that traveles for 13sec from point of origin to the viewer.
At the viewer it still sound like the wave was supersonic (through a video).

2tts,

I'm trying to understand what exactly you are trying to do. Are you:
A) calculating a distance by determining the difference between when you see something and when you hear it?
or
B)calculating a distance by determining the difference between when you see something and a super sonic blast wave hits you?

If it is the former, this should be an easy calculation, since nothing is moving - neither you, the listener, or the thing creating the sound - the source object. Yes, you can use the speed of sound vs the speed of light [if that really matters at all - you can probably assume it being simultaneous] to get your calculation.
We do this all the time when figuring out how far away a storm is - when you see lightning you can count the seconds until you hear the thunder. 3 seconds is roughly 1 km.

If it is the latter, I do not think you would be able to easily determine how fast something is moving if it is supersonic - unless someone else can say otherwise?

2tts said:
To calculate the distance from a stationary visible object using the speed of sound when dealing with a supersonic blast wave from that object, how would one proceed?
Is the standard 340m/s good enough reference?
How is the velocity reduction over time and distance?

Does all the variables (temperature, elevation and such) have a notable impact on velocity reduction?
For these examples let's say sea level at 20C.

Example 1:
Looking at a large amount of high exploive, TNT, going off from far away, say 5km. How to calculate distance?

Example 2:
This is what triggerd me into reserching this.
A volcano eruption caused a shock wave that traveles for 13sec from point of origin to the viewer.
At the viewer it still sound like the wave was supersonic (through a video).

This document from FEMA implies that the supersonic blast wave only lasts for a few milliseconds as it expands outward from the high explosive (HE) or other source:

So it's not supersonic for very long, and if you are several seconds away from it, it sounds like using the standard speed of sound (adjusted for temperature) would be fairly accurate.

fishspawned said:
2tts,

I'm trying to understand what exactly you are trying to do. Are you:
A) calculating a distance by determining the difference between when you see something and when you hear it?
or
B)calculating a distance by determining the difference between when you see something and a super sonic blast wave hits you?

I was thinking of the two as the same thing, as in looking at the thing go off, then "hearing" the supersonic wave.

fishspawned said:
We do this all the time when figuring out how far away a storm is - when you see lightning you can count the seconds until you hear the thunder. 3 seconds is roughly 1 km.

Yes I've done this myself with thunderstorms. But when dealing with the lightning you get that distinct loud crackle(blast wave) that i would say is supersonic when struck close by.
But at a distance(not really far away) its clearly just dark rumbling, which i would guess is subsonic.
From this i get that thunder is only supersonic for a short duration.
Am i correct at assuming this?

fishspawned said:
If it is the latter, I do not think you would be able to easily determine how fast something is moving if it is supersonic - unless someone else can say otherwise?

That is where i am running into problems.
Or is there a wave traveling behind the supersonic blast wave at normal 340m/s that we can use for calculating?
berkeman said:
This document from FEMA implies that the supersonic blast wave only lasts for a few milliseconds as it expands outward from the high explosive (HE) or other source:

So it's not supersonic for very long, and if you are several seconds away from it, it sounds like using the standard speed of sound (adjusted for temperature) would be fairly accurate.

Well to me it sounds like maybe they are talking about the duration "the listener" is in the wave as it passes by..

If it is supersonic for such a short time, then why do we still hear what sounds like a sonic boom at a great distance from the object??
What kills everything for me with the volcano thing is that by timing the wave as it decends down the mountain, it looks to do about 223m(volcano height according to wiki) in about a sec or maybe more... But it still sounds so much like its the supersonic boom at a distance of 13sec. Explenation?

Video in question:

2tts,

I watched the video, but i am not convinced that this is a sonic boom, or rather a shock wave hitting the boat. First off, what I seem to see going on in the video, is a large explosion - very very loud one - where the sound reaching the people in about 13 seconds. This is august 2014 in Papua New Guinea 0 which at that month had a mean temperature of 28 degrees C. - which tells us that the sounds was traveling around 348.3 m/s and therefore the blast took place roughly 4.53 km away - this seems reasonable by what I see in the video. A shock wave generally - as stated earlier in this thread - dissipates quickly so it is unlikely it would be a shock wave 4 and a half km after it started.

2tts said:
I was thinking of the two as the same thing, as in looking at the thing go off, then "hearing" the supersonic wave.
Ok, then this is fine. I think really you are simply looking in the wrong places for sonic booms. They are generally made by moving objects. Which makes the whole business of finding out where they are a moot point. You are interested in stationary objects making shock waves that do not reduce in energy over distance and i am afraid this is unlikely to be happening.

2tts said:
Or is there a wave traveling behind the supersonic blast wave at normal 340m/s that we can use for calculating?
I believe - now correct me if I'm wrong - that this is what i did just now when looking at your video. I find it likely that you are looking at nothing more than the sound of the initial blast having traveled towards the camera at the speed of sound.

I think what you are thinking is to be a sonic boom is really just an incredibly loud explosion. It may be very loud, but it is not necessarily a sonic boom.

I hope this helps.

So basicly most of my thoughts are invalid because the wave is only supersonic for a very short duration, if at all.
Hmm

berkeman
2tts,

Perhaps, but you may also put an entirely positive spin on this and consider that this makes your calculations much much easier!

Another way to look at this is by using real numbers. Atmospheric pressure is roughly 100000 Pa. 100 Pa (1 part in a thousand) of over pressure corresponds to 133db (130db corresponds to a jet engine at 100 ft). So your calculation is essentially a far field calculation. Shock velocity is needed when you need to make near field corrections. For example a 1kton explosion at 1km has an average sound speed of 423 m/s with a Mach number of 1.034 while at 5 km 357 m/s with a Mach number of 1.004 (for air with a sound speed of 340 m/s)

Oops, the blast numbers came from Kinney and Graham Explosive Shocks in Air

## 1. What is a supersonic wave?

A supersonic wave is a type of sound wave that travels faster than the speed of sound. This means that the wave is traveling at a speed greater than 343 meters per second in air at sea level.

## 2. How is the speed of a supersonic wave calculated?

The speed of a supersonic wave can be calculated using the formula v = c x M, where v is the wave's speed, c is the speed of sound in the medium, and M is the Mach number. The Mach number is the ratio of the wave's speed to the speed of sound in that medium.

## 3. What factors affect the distance a supersonic wave can travel?

The distance a supersonic wave can travel is affected by several factors, including the medium it is traveling through, the temperature and pressure of the medium, and the amount of energy in the wave.

## 4. How does temperature affect the speed of a supersonic wave?

Temperature affects the speed of a supersonic wave because it affects the speed of sound in the medium. As the temperature increases, the molecules in the medium move faster, causing the speed of sound to increase. This, in turn, increases the speed of the supersonic wave.

## 5. Why is it important to calculate the distance of a supersonic wave?

Calculating the distance of a supersonic wave is important for a variety of reasons. It can help determine the range of a supersonic weapon, the distance at which a supersonic plane can break the sound barrier, and the potential damage caused by a supersonic wave. It is also crucial for understanding and studying the properties of supersonic waves and their behavior in different environments.

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