Frustrated with Physics: Measuring Temperature Changes in the Ocean

[lostie100]

Ok. At a depth of 1000m, the ocean temp is 4 degrees celsius and the speed of sound is 1480m/s. From lab experiments, for every 4m/s increase in velocity, the temp increases by 1 degrees.
When the distance is 8000km, the smallest time change that can be detected is 1s, what is the smallest temp change that can be measured?

I am so frustrated w/ this question.

 

[LowlyPion]

Ok. At a depth of 1000m, the ocean temp is 4 degrees celsius and the speed of sound is 1480m/s. From lab experiments, for every 4m/s increase in velocity, the temp increases by 1 degrees.
When the distance is 8000km, the smallest time change that can be detected is 1s, what is the smallest temp change that can be measured?

I am so frustrated w/ this question.

Start with the smallest speed change you can effectively measure. If you can't resolve a sound wave that travels 8 x 10^6 m and know within 1 second when it started then you can't measure any finer scale of speed than that can you? So what would that be in terms of the smallest "increment" of speed that you can represent?

Knowing that can't you figure the smallest temp change that you can reliably record if you are basing your measurement on the measured speed?

 

[Moetasim]

I understand your frustration with this question. Measuring temperature changes in the ocean can be a complex and challenging task. However, it is important to approach this problem with a systematic and scientific approach.

To determine the smallest temperature change that can be measured, we need to use the information given in the question and apply some mathematical calculations. Firstly, we know that at a depth of 1000m, the temperature is 4 degrees Celsius and the speed of sound is 1480m/s. We also know from lab experiments that for every 4m/s increase in velocity, the temperature increases by 1 degree.

Based on this information, we can calculate the velocity of sound at a depth of 8000km using the given formula: V = d/t, where V is the velocity, d is the distance, and t is the time. Plugging in the values, we get V = 8000000/1 = 8000000m/s.

Next, we need to calculate the change in velocity from 1480m/s to 8000000m/s, which is 7998520m/s. We can then use this value to calculate the corresponding change in temperature using the given relationship of 1 degree change for every 4m/s increase in velocity. This gives us a change in temperature of 1999630 degrees Celsius.

However, this value may seem unrealistic as it is much higher than the highest known temperature on Earth. This is because the given values and calculations assume a linear relationship between velocity and temperature, which may not be accurate in real-world scenarios.

In conclusion, it is important to approach scientific problems with caution and to critically evaluate the given information. While this calculation may provide a theoretical answer, it may not reflect the actual smallest temperature change that can be measured in the ocean. Further research and experimentation may be needed to determine the most accurate and reliable method for measuring temperature changes in the ocean.