Solving Sound Questions: Mach Number, Echo Sonar, Concert Delay

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In summary: Assume you visit a world where the atmosphere is made up of hydrogen. Your spacecraft can fly Mach 20 on Earth, as measured by sound at 5degreesC. On this planet, what is your Mach number if the speed of sound in hydrogen is 1267m/s?2. What is the Mach number for a shuttle if it starts re-entry after traveling around Earth in 1.495h at an orbital radius of 6.73 x 10^6m?Assume that the air temperature is -30degreesC.3. On a hot summer night (32degreesC) you are listening to a rock group in a stadium 350m
  • #1
jnimagine
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I have a few questions about my hw...

1. Assume you visit a world where the atmosphere is made up of hydrogen. Your spacecraft can fly Mach 20 on Earth, as measured by sound at 5degreesC. On this planet, what is your Mach number if the speed of sound in hydrogen is 1267m/s?

2. What is the Mach number for a shuttle if it starts re-entry after traveling around Earth in 1.495h at an orbital radius of 6.73 x 10^6m?
Assume that the air temperature is -30degreesC.

3. On a hot summer night (32degreesC) you are listening to a rock group in a stadium 350m away. Your friend is sitting in an air-conditioned room across the country, listening to broadcast radio. If the signal travels 30,000km up to a satellite that retransmits it, who hears the concert first?

4. Determine the depth of water if an echo using sonar returs in 870ms and the speed of sound in water is 5300km/h

I tried to do these questions but i really can't figure it out... T.T

Any help would be appreciated...^^
Thank you
 
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  • #2
Please provide your attempts on the questions and from there help can be provided!
 
  • #3
well the first two i don't have any idea... T.T
but the last two i did do

3. first, v= 3.0 x 10^8m/s + (0.6)(32deg.C)
= 3.0 x 10^9m/s
t=d/v
= 350m/3.0x10^9m/s
= 1.16 x 10^-7
then, t=d/v
= 3.0x10^7m/3.0x10^9m/s
= 0.010s
therefore, i hear the concert first...
but i don't think it's right...
the answer says that it takes 1.00s for for the first calculation

4. t=0.87s d=vt
v=1472.2m/s = (1472.2m/s)(0.87s)
= 1280.8m
the answer's 640m...
 
  • #4
1.
Check out wikipedia.org for info about what mach numbers are. If speed of sound is used to define the mach number what happens if the speed of sound changes?

2.
No idea what 1.495h is :/

3.
The velocity regarding 350m is not the speed of light, it is the speed of sound... around 350m/s i believe. The second calculation seems correct.

Yes 350/350 would give you 1s thus he would hear it first not you.

4.
The total distance traveled is 1280.8m yes but how do echoes work? They go there and back? thus...?
 
  • #5
ponjavic said:
1.
Check out wikipedia.org for info about what mach numbers are. If speed of sound is used to define the mach number what happens if the speed of sound changes?

2.
No idea what 1.495h is :/

1. so if the speed of sound increases, mach number increases and it would become supersonic..? and if it decreases, it becomes subsonic?

2. I believe 1.495h means 1.495 hours...
 
  • #6
jnimagine said:
1. so if the speed of sound increases, mach number increases and it would become supersonic..? and if it decreases, it becomes subsonic?

2. I believe 1.495h means 1.495 hours...

1.
Erm I guess, doesn't really matter.

Mach means V/Vsound

Thus 20Mach would mean V=20*Vsound

Now what's the new mach number in the hydrogen: mind that Vsound changed

Mach number = V/Vsound(in hydrogen)

2.
havent got a clue
 
  • #7
ponjavic said:
1.
Erm I guess, doesn't really matter.

Mach means V/Vsound

Thus 20Mach would mean V=20*Vsound

Now what's the new mach number in the hydrogen: mind that Vsound changed

Mach number = V/Vsound(in hydrogen)

2.
havent got a clue

um... i get a wrong answer...
this is what i did...
v= (332 +0.6(5degC))m/s
= 335m/s
Mach= v of hydrogen / v
= 1267m/s / 335m/s
= 3.78

the answer's 5.29... what did i do wrong??
and one more quick question...
For the final answer for mach number how many sig figs do i have to have? should it be 4 because 5degC has the least amt of digits so the final answer only has one sig fig? or... I'm so confused with sig figs now...T.T
 
  • #8
From
jnimagine said:
2. What is the Mach number for a shuttle if it starts re-entry after traveling around Earth in 1.495h at an orbital radius of 6.73 x 10^6m?
Assume that the air temperature is -30degreesC.

I tried to do these questions but i really can't figure it out... T.T

Any help would be appreciated...^^
Thank you

if you know the radius of the shuttle's orbit and the time it takes to complete an orbit, you can calculate its orbital speed. that's simple math.

if you assume that upon re-entry that speed doesn't change, and at whatever altitude it "re-enters" the atmosphere, the speed of sound is the same as that of air at -30 degrees C, it's pretty straighforward to calculate how many times the speed of sound it's going at re-entry.

does framing the question in those kinds of words and sentences help?

see if you can get help from others here or from your teachers/instructors/professors on how to reword the given information so that the solutions are easier to frame.

+af
 
  • #9
From
jnimagine said:
I have a few questions about my hw...

1. Assume you visit a world where the atmosphere is made up of hydrogen. Your spacecraft can fly Mach 20 on Earth, as measured by sound at 5degreesC. On this planet, what is your Mach number if the speed of sound in hydrogen is 1267m/s?

I tried to do these questions but i really can't figure it out... T.T

Any help would be appreciated...^^
Thank you

Similarly, if the spacecraft files at Mach 20 "on earth" (over the earth), how many m/s or km/h is its ground speed?

if it flies at that ground speed on the planet with the H2 atmosphere, what's its Mach speed?


not so hard when you say it that way?

again, +af
 
  • #10
plusaf said:
From

if you know the radius of the shuttle's orbit and the time it takes to complete an orbit, you can calculate its orbital speed. that's simple math.

if you assume that upon re-entry that speed doesn't change, and at whatever altitude it "re-enters" the atmosphere, the speed of sound is the same as that of air at -30 degrees C, it's pretty straighforward to calculate how many times the speed of sound it's going at re-entry.

does framing the question in those kinds of words and sentences help?

see if you can get help from others here or from your teachers/instructors/professors on how to reword the given information so that the solutions are easier to frame.

+af

i get a wrong answer...T.T
this is what i did:
v=d/t
=6.73x10^6m/s / 5382s
= 1260.46m's

v=(332+0.6T)m/s
= (332 + 0.6(-30degC))m/s
= 314m/s

Mach = 1250.46m/s / 314m/s
= 4.0

the answer's 25...
 
  • #11
plusaf said:
From

Similarly, if the spacecraft files at Mach 20 "on earth" (over the earth), how many m/s or km/h is its ground speed?

if it flies at that ground speed on the planet with the H2 atmosphere, what's its Mach speed?


not so hard when you say it that way?

again, +af

v= (332 +0.6(5degC))m/s
= 335m/s
Mach= v of hydrogen / v
= 1267m/s / 335m/s
= 3.78

um... is this how you do it?
well i guess not cause the answer's wrong lol
the answer's 5.29...

and in this case how many sig figs would the final answer have?
 
  • #12
jnimagine said:
v= (332 +0.6(5degC))m/s
= 335m/s
Mach= v of hydrogen / v
= 1267m/s / 335m/s
= 3.78

um... is this how you do it?
well i guess not cause the answer's wrong lol
the answer's 5.29...

and in this case how many sig figs would the final answer have?
Mach number is the speed of the object (v) divided by the speed of sound (u)

M = v/u = 20 in air where, by your calculation, u = 335m/s

v = 20u = ___________

In hydrogen, where the sound speed is u' = 1267m/s the mach number will be

M' = v/u' = ____________
 
  • #13
OlderDan said:
Mach number is the speed of the object (v) divided by the speed of sound (u)

M = v/u = 20 in air where, by your calculation, u = 335m/s

v = 20u = ___________

In hydrogen, where the sound speed is u' = 1267m/s the mach number will be

M' = v/u' = ____________

thank you so much older dan
i get it now! > . <
but how many sig figs should my final answer have? it's confusing cause there were many steps involved in this...

can u help me with #4 by any chance?
i tried to do it, u'll see my posts above... but i get a wrong answer...T.T
 
  • #14
jnimagine said:
thank you so much older dan
i get it now! > . <
but how many sig figs should my final answer have? it's confusing cause there were many steps involved in this...

can u help me with #4 by any chance?
i tried to do it, u'll see my posts above... but i get a wrong answer...T.T
Not more than 3 on the significant figures. It's hard to say when a problem gives a number like 20 how they want you to take it. Do they mean within 5 of 20, or 20 +- .5, or 20.0 or ? When in doubt, I usually go with 3, and since you have your sound speed to 3, I would go with that.

Problem #4 is just a distance, speed, time problem. The sound has to travel down and back, so the distance is twice the depth of the water, at the speed given in the problem, in the time specified. Just be careful with the units. Convert km/hr to km/sec or m/sec and ms (milliseconds) to seconds.
 
  • #15
OlderDan said:
Not more than 3 on the significant figures. It's hard to say when a problem gives a number like 20 how they want you to take it. Do they mean within 5 of 20, or 20 +- .5, or 20.0 or ? When in doubt, I usually go with 3, and since you have your sound speed to 3, I would go with that.

Problem #4 is just a distance, speed, time problem. The sound has to travel down and back, so the distance is twice the depth of the water, at the speed given in the problem, in the time specified. Just be careful with the units. Convert km/hr to km/sec or m/sec and ms (milliseconds) to seconds.

oh oops i get #4 i meant #2 :redface:
 
  • #16
jnimagine said:
oh oops i get #4 i meant #2 :redface:
Can you find the speed from the given orbital radius and the period?
 

Related to Solving Sound Questions: Mach Number, Echo Sonar, Concert Delay

1. What is Mach Number and why is it important in sound?

Mach Number is a measure of an object's speed relative to the speed of sound in the medium it is traveling through. In sound, it is important because it determines whether an object will produce a sonic boom or not. When an object travels at or above the speed of sound, the air molecules in front of it get compressed, creating a shock wave that we hear as a loud boom.

2. How does echo sonar work?

Echo sonar uses sound waves to detect objects in the water. It works by emitting high-frequency sound waves from a device called a transducer, which then travel through the water. When these sound waves hit an object, they bounce back and are detected by the transducer. The time it takes for the sound waves to bounce back is used to calculate the distance to the object.

3. What is concert delay and why is it used?

Concert delay is a technique used in live music performances to ensure that all members of the audience hear the sound at the same time. It involves using multiple speakers placed at different distances from the stage, with each speaker playing the same sound at slightly different times. This creates a "delay" effect, where the sound reaches each section of the audience at the same time, creating a more balanced and immersive listening experience.

4. How does the speed of sound change in different mediums?

The speed of sound is affected by the density and elasticity of the medium it is traveling through. In general, sound travels faster in denser and more elastic mediums, such as solids, and slower in less dense and less elastic mediums, such as gases. For example, sound travels about four times faster in water than in air.

5. What factors can affect the accuracy of sound measurements?

Several factors can affect the accuracy of sound measurements, including temperature, humidity, and atmospheric conditions. Sound waves travel at different speeds in different temperatures and humidity levels, which can affect the measurements. Additionally, wind and other environmental factors can also impact the accuracy of sound measurements.

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