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Answer :
The surface of the snow is approximately 0.466 meters from the sonic depth gauge.
To find out how far the surface of the snow is from the sonic depth gauge, we can follow these steps:
Understanding the Setup: The sonic depth gauge is positioned 4.3 meters above the ground. It sends an ultrasound pulse downward toward the snow and measures how long it takes for that pulse to reflect back.
Calculating the Speed of Sound: The speed of sound in air is affected by temperature. At -20°C, the speed of sound can be calculated using the formula:
v = 331.5 + (0.6 x temperature in °C)
Therefore, for -20°C:
[tex]v \approx 331.5 + (0.6 \times -20)\\ \approx 331.5 - 12 \\= 319.5 \text{ m/s}[/tex]
Considering the Time of Flight: The ultrasound pulse takes 0.024 seconds to complete its journey to the snow and back to the gauge. Since this time is for a round trip, we must divide by 2 to find the time taken to reach the snow:
[tex]\text{Time to snow} = \frac{0.024}{2} = 0.012 \text{ seconds}[/tex]
Calculating the Distance to the Snow: We can then find the distance to the snow using the speed of sound and the time taken to reach the snow:
Distance to snow} = v x Time to snow
Distance to snow = 319.5 m/s x 0.012s
= 3.834 m
Finding the Height of Snow Surface from the Gauge: The distance from the sonic depth gauge to the surface of the snow is approximately 3.834 meters. Since the gauge is 4.3 meters above the ground, the height of the snow surface from the gauge is found by:
Height of snow from gauge = 4.3 - 3.834
= 0.466 m
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Rewritten by : Barada
To find the distance to the snow surface, the speed of sound at -20 degrees Celsius is calculated and used along with the ultrasound pulse travel time. This results in a distance of approximately 1.916 meters from the device to the snow.
To calculate the distance to the surface of the snow from the device, we need to know the speed of sound in air at the specified temperature (-20°C). The speed of sound in air at 20°C is commonly known to be approximately 343 m/s. However, the speed decreases when the temperature is lower. The speed of sound at a specific temperature can be estimated using the formula:
V = 331.4 + (0.6 imes T)
where V is the speed of sound in m/s and T is the temperature in degrees Celsius. For -20°C:
V = 331.4 + (0.6 imes -20) = 319.4 m/s
The time it took for the ultrasound pulse to travel down to the snow and back up to the device is given as 0.024 seconds. The distance traveled by the sound wave in this time is:
D = V imes t
However, since the wave travels to the snow and then back to the device, the actual distance from the device to the snow is half this value. So, the distance to the snow surface is:
D = (V imes t) / 2 = (319.4 m/s imes 0.024 s) / 2
D = 3.8328 m / 2
D = 1.9164 m
Therefore, the snow surface is approximately 1.916 m from the device, rounded to three significant figures.
