Rock Group Performs in Bar: How Far Can You Hear?

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In summary, the music at a bar can be heard at a distance of 3640 kilometers with an intensity of just over 166.5564633 watts per meter squared.
  • #1

Homework Statement


A rock group is playing in a bar. Sound
emerging from the door spreads uniformly in
all directions. The intensity level of the music
is 116 dB at a distance of 5.77 m from the
door.
At what distance is the music just barely
audible to a person with a normal threshold
of hearing? Disregard absorption.
Answer in units of m.

So,
Given-
I1(dB) (the intensity level 5.77 meters from the door)=116 dB
r1 (distance from door when intensity is 116 dB)= 5.77 m
Io (Intensity at threshold of hearing)= 1e-12

Unknown-
r2 (Radius at threshold of hearing)
P (power of sound source)
I1(w/m^2) (intensity 5.77 meters from door in watts/meters squared)

Homework Equations


dB=10log(I/Io)
P=4*I*π*r^2
r=√(P/4πI)

The Attempt at a Solution


First, I changed the given Intensity into W/m^2 instead of hertz.

dB=10log(I1/Io)
116=10log(I1/1e-12)
11.6=log(I1/1e-12)
10^11.6=I1/1e-12
(1e-12)(10^11.6)=I1

.3981071706=I1

So that's the Intensity at the spot from the door mentioned, so now I calculated the power source.

P=4*I1*π*r1^2
P=4*.3981071706*π*5.77^2

P=166.5564633

So, now that I had the power source, I calculated the radius needed to achieve threshold of hearing

r2=√(P/4πIo)
r2=√(166.5564633/4*π*1e-12)
r2=√(166.5564633/1.256637061e-11)
r2=√1.325414222e13

r2=3640623.878

Doesn't seem right... 3.6 million miles seems overkill.
 
Last edited:
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  • #2


stevenbhester said:
Doesn't seem right... 3.6 million miles seems overkill.

I think you mean 3.6 million meters. :wink:
 
  • #3


Oops, typo... question still stands though :)
 
  • #4


Could you help with my question though please?
 
  • #5


stevenbhester said:
Oops, typo... question still stands though :)

It may seem like a lot, I agree. But 116 dB is pretty loud, and we are ignoring absorption and all that. :cool: I mean it's really only 3640 km. That's just peanuts compared to the size of, say, the galaxy.

Seriously though, I don't see any mistakes with your math. There is a much easier way to solve this problem, but the answer comes out the same as yours.

Edit:
Okay, I'll bite with the easier solution. After all, you did already get the answer.

Note that I'll use 0 dB use the human threshold of hearing. In other words,

[tex] 0 \ \textbox{dB} = 10 \ \textbox{log} \left( \frac{I_0}{I_0} \right) [/tex]

Also take note that

[tex] I \propto \frac{1}{r^2} [/tex]

So construct the problem as you have already done,

[tex] 116 \ dB = 10 \ \textbox{log} \left( \frac{I_1}{I_0} \right) [/tex]

Now note that at some distance r2 we're going to end up with an intensity I0

So we can say,

[tex] I_0 \propto \frac{1}{(r_2)^2} [/tex]

and

[tex] I_1 \propto \frac{1}{(r_1)^2} = \frac{1}{(5.77 m)^2}[/tex]

So make your appropriate substitutions, and note that

[tex] 10 \ log \left( x^2 \right) = 20 \ log \left( x \right) [/tex]

Solve for r2.
 
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  • #6


Thanks, I guess the website is at fault. It maintains that I'm wrong. :(
 

1. How far can sound travel?

The distance that sound can travel depends on several factors, such as the volume of the sound, the type of medium it is traveling through, and the atmospheric conditions. In general, sound can travel a few miles in ideal conditions.

2. What is the role of atmospheric conditions in sound travel?

Atmospheric conditions, such as temperature, humidity, and wind, can affect the speed and distance that sound can travel. For example, sound travels faster in warm air compared to cold air, and it can also travel farther in calm conditions compared to windy conditions.

3. How loud is a rock group performing in a bar?

The loudness of a rock group performing in a bar can vary depending on the size of the bar, the amplification of the sound, and the distance from the stage. Generally, it can range from 90-110 decibels, which is considered very loud and can potentially cause hearing damage.

4. How far can you hear a rock group performing in a bar?

The distance at which you can hear a rock group performing in a bar also depends on the factors mentioned earlier, such as the loudness of the performance and atmospheric conditions. In general, you may be able to hear it a few blocks away from the bar, but the sound will become fainter as you move farther away.

5. Can sound travel through all types of mediums?

No, sound cannot travel through all types of mediums. It needs a medium, such as air, water, or solids, to travel. For example, sound cannot travel through a vacuum, as there is no medium for it to vibrate through.

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