Speed of sound and sound detection lag between ears

In summary, the problem was trying to use the cosine law to calculate the length of the hypotenuse when v=d/t needs to be flipped.
  • #1
aliaze1
174
1

Homework Statement



One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45 degrees to your right.

What is the difference in arrival times? Give your answer in microseconds.

Homework Equations



v=d/t
speed of sound in air @ rm temp = 343m/s

The Attempt at a Solution



I set up the problem as so:

http://photo.ringo.com/230/230995202O179609724.jpg [Broken]

http://photo.ringo.com/230/230995202O179609724.jpg

http://photo.ringo.com/230/230995202O179609724.jpg [Broken]

and then calculated the two dark red lines as different hypotenuses of the two different triangles (one is L+0.1 and the other is L-0.1), then I used v=d/t (with some manipulations) and got a difference which was incorrect

then i tried to set it up as 5 being the main hypotenuse (dashed turquoise), and did a similar process, again wrong
 
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  • #2
I believe the 5m should be along the dashed 45 degree line... Use the cosine law to calculate the length of the two sides...

Use the dashed line, 0.1m and the right hypoteneuse triangle... calculate the length of the hypoteneuse...

Then use the dashed line, 0.1m and the left hypoteneuse triangle... calculate the length of the left hypoteneuse...
 
  • #3
i have forgotten that way, but try drawing a per. line to the last dark red line from L-0.1 point,
and you make a safe assumption that two red lines are parallel..
kinda that

it's a square, in case you don't know
and, so using Pythagorean theorem I got 4.12286E-4 s,

and using some approximations, i made it a two lines problem, and got something very similar.

(0.2*5)/5 = difference in length
 
Last edited:
  • #4
learningphysics said:
I believe the 5m should be along the dashed 45 degree line... Use the cosine law to calculate the length of the two sides...

Use the dashed line, 0.1m and the right hypoteneuse triangle... calculate the length of the hypoteneuse...

Then use the dashed line, 0.1m and the left hypoteneuse triangle... calculate the length of the left hypoteneuse...

After doing so, since v=d/t and i want t, i need to flip the velocity, hence making it 1/343
 
  • #5
...not working...
 
  • #6
but I am pretty sure that L is 5 m.
 

1. What is the speed of sound?

The speed of sound is the distance that sound travels in a certain amount of time. In dry air at 20°C, the speed of sound is approximately 343 meters per second.

2. How does the speed of sound differ in different materials?

The speed of sound can vary depending on the material it is traveling through. For example, sound travels faster through solids than through liquids or gases. The speed of sound also depends on factors such as temperature, density, and elasticity of the material.

3. Why is there a lag in sound detection between our ears?

The lag in sound detection between our ears is due to the distance between them. Sound waves travel at a finite speed, so it takes a certain amount of time for the sound to reach our ears. This difference in time allows our brain to determine the direction and location of the sound.

4. What is the importance of understanding the speed of sound and sound detection lag between ears?

Understanding the speed of sound and sound detection lag between ears can help us determine the location of a sound source and the direction it is coming from. This can be useful in various fields such as navigation, animal behavior studies, and sound engineering.

5. How can we measure the speed of sound and sound detection lag between ears?

The speed of sound can be measured using a variety of methods, such as using a stopwatch to measure the time it takes for sound to travel a known distance. The sound detection lag between ears can be measured by playing a sound in one ear and recording the time it takes for the individual to perceive the sound in the other ear.

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