Sound Problem: Find Distance

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In summary, the conversation is discussing how to use equations to determine the depth of a lake based on the time it takes for a sound pulse to travel from the surface to the bottom and back. The speed of sound in air and water are given, as well as the air and water temperatures. The equation for determining depth is provided and the conversation clarifies the use of "20" in the calculations.
  • #1
mukimuki2
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problem How and which equation?? Please help me!
At a height of 10 meters above the surface of a lake, a sound pulse is generated. The echo from the bottom of the lake returns to the point of origin 0.140 s later. The air and water temperatures are 20°C. How deep is the lake?



equations
d=vt
v=wavelength*frequency
wavelength = 4(L + 0.4d)
Vsound = 331.5m/s + .6T

ok here's what I got from a friend and I know its right but...
Speed in air: 343 m/s Speed in water: 1482 m/s

Time in air = 20/343 = 0.058 s
Time in water = 0.140 - 0.058 = 0.082 s
Time to hit bottom: 0.082 / 2 = 0.041 s
d = 1482 (0.041) = 60.8 m

...where did the 20 come from on "Time in Air"? is it 10 x 2?
 
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  • #2
Yes, 20 is 10 x 2. The speed of sound in air is 343 m/s and the time for the sound pulse to travel 10 meters is 10/343 = 0.029 s. Therefore, the time for the sound pulse to travel 20 meters is 0.058 s (0.029 x 2).
 
  • #3



Hello there,

Thank you for reaching out for help with your sound problem. The equation you will need to use in this case is the distance formula, d=vt, where d is the distance, v is the speed of sound, and t is the time it takes for the sound pulse to travel.

To solve this problem, you will first need to calculate the speed of sound in both air and water at a temperature of 20°C. The equations you provided for speed in air and water are correct, so we can use those values.

Next, we can calculate the time it takes for the sound pulse to travel in air and water. Since the total time for the pulse to travel and return is 0.140 seconds, we can divide this by 2 to get the time for one leg of the journey. This gives us a time of 0.070 seconds for the sound pulse to travel from the point of origin to the bottom of the lake.

Now, we can plug in the values we have calculated into the distance formula. The speed of sound in water is 1482 m/s, and the time it takes for the sound pulse to travel in water is 0.070 seconds. This gives us a distance of 103.74 meters for the depth of the lake.

To answer your question about the 20, this is the temperature given in the problem. The speed of sound is affected by temperature, so we need to use the correct value for the temperature in our calculations. In this case, we are using 20°C as the temperature for both air and water.

I hope this explanation helps you understand the problem and how to solve it. If you have any further questions, please don't hesitate to ask. Good luck with your studies!
 

1. How does sound travel through different mediums?

Sound travels through different mediums by creating vibrations. These vibrations travel through the medium in a wave-like motion, causing molecules to bump into each other and pass the energy along.

2. What factors affect the speed of sound?

The speed of sound is affected by the medium it is traveling through, temperature, and humidity. Sound travels faster through denser mediums and at higher temperatures and humidity.

3. How do we measure the distance of a sound?

To measure the distance of a sound, we can use the speed of sound and the time it takes for the sound to travel to calculate the distance. The formula is distance = speed of sound x time.

4. Can sound travel through a vacuum?

No, sound cannot travel through a vacuum because there are no molecules to vibrate and carry the sound waves.

5. How can we use sound to find distance?

We can use a technique called echolocation, where we emit a sound and measure the time it takes for the sound to bounce back to us. By knowing the speed of sound, we can calculate the distance based on the time taken.

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