Solving Sound Waves Problem: Direction of Sound Origination

In summary, the problem discussed is how our brain perceives sound direction and how technology can create an illusion of sound coming from a specific direction. Using the concept of time delay and the speed of sound, we can calculate the angle at which a sound appears to originate based on the time delay between our two ears. In this particular scenario, the sound appears to come from an angle of 43.6 degrees to the left of the center.
  • #1
kreil
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The problem is this:

Only two recording channels are needed to create the illusion of sound coming from any point located between two speakers of a stereophonic sound system. If the same signal is recorded in both channels, a listener will hear it coming from a single direction halfway between the two speakers. The brain can sense the direction of sound by noting how much earlier a sound is heard in one ear than in the other.

Model your ears as two sensors 19.0cm apart in a flat screen. If a click from a distant source is heard 210 microseconds earlier in the left ear than in the right, from what direction does it appear to originate?


Intuitively, I know that the sound will appear to come from left of the center, but I need to find the exact angle to the left that it originates. I'm not sure where to start in the way of formulas. I figured it might be a trig problem but the way I set it up on paper didn't allow for finding many sides of the triangles. Any help is appreciated.

Josh
 
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  • #2
, thank you for bringing up this interesting problem. I am always fascinated by how our brains perceive sound and the role of technology in creating an illusion of sound direction.

To solve this problem, we can use the concept of time delay and the speed of sound. The speed of sound in air is approximately 343 meters per second. Since the two sensors (our ears) are 19.0cm apart, the time delay between the two ears can be calculated using the formula: t = d/v, where t is the time delay, d is the distance between the sensors, and v is the speed of sound.

In this case, t = (0.19m)/(343m/s) = 0.00055 seconds = 550 microseconds.

Now, we know that the actual time delay is 210 microseconds, which means the sound source is creating an additional time delay of 340 microseconds (550-210). This additional time delay is due to the sound traveling from the source to the sensors.

To find the angle at which the sound appears to originate, we can use the formula: tanθ = O/A, where θ is the angle, O is the opposite side (distance between the sensors), and A is the adjacent side (distance from the center to the source).

Plugging in the values, we get: tanθ = (0.19m)/A

Using the Pythagorean theorem, we can find the value of A: A = √(0.19m)^2 + (340 microseconds)*(343m/s) = 0.20m

Now, plugging in the values for A, we get: tanθ = (0.19m)/0.20m = 0.95

Taking the inverse tangent, we get: θ = 43.6 degrees

Therefore, the sound appears to originate from an angle of 43.6 degrees to the left of the center. I hope this helps you understand the problem better and gives you a starting point for finding the exact angle. Happy experimenting!
 

1. How do you determine the direction of sound origination?

The direction of sound origination can be determined by using techniques such as triangulation, where the sound is measured from multiple locations and the intersection of those measurements is used to pinpoint the source. Other methods include using specialized equipment such as microphones with directional sensitivity or analyzing the phase differences of the sound waves at different locations.

2. What factors can affect the accuracy of determining the direction of sound origination?

Several factors can affect the accuracy of determining the direction of sound origination, including the presence of background noise, the distance between the source and the measuring equipment, and the type of surface the sound is traveling through. Additionally, the quality and sensitivity of the measuring equipment can also impact the accuracy of the results.

3. Can sound originate from multiple directions?

Yes, sound can originate from multiple directions, making it important to use multiple measurement techniques to accurately determine the source. In some cases, the sound may also reflect off of surfaces, creating the perception of multiple directions of origination.

4. Are there any limitations to using sound to determine direction of origination?

While sound can be a useful tool in determining the direction of origination, there are some limitations to consider. For example, sound waves can be easily affected by environmental factors such as wind or temperature, which can impact the accuracy of the measurements. Additionally, the speed of sound can vary depending on the medium it is traveling through, which can also affect the results.

5. How can the direction of sound origination be applied in real-world scenarios?

The ability to accurately determine the direction of sound origination can have practical applications in various fields such as engineering, architecture, and environmental studies. For example, it can be used to locate the source of noise pollution in a city or to design buildings that minimize noise disturbance. It can also aid in detecting potential hazards, such as identifying the direction of an approaching storm or locating the source of a potential explosion.

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