Question

How many seconds would it take an echo sounder's ping to make the trip from a ship to the Challenger Deep \((10,994\) meters \()\) and back? Recall that depth \(=1 / 2(1500 \mathrm{~m} / \mathrm{sec} \times\) echo travel time \()\)

Short answer

The echo travel time is approximately 14.66 seconds.

Step-by-step solution

Understand the Formula

The formula given is \( \text{depth} = \frac{1}{2} (1500 \, \text{m/sec} \times \text{echo travel time}) \). This indicates that the round trip time is used in the calculation.

Identify Known Values

We know the depth, \( \text{depth} = 10,994 \, \text{meters} \), and the speed of sound in water is \( 1500 \, \text{m/sec} \).

Isolate Echo Travel Time

Rearrange the equation to find the echo travel time: \( \text{echo travel time} = \frac{2 \times \text{depth}}{1500} \).

Substitute Known Values

Plug the given depth into the formula: \( \text{echo travel time} = \frac{2 \times 10,994}{1500} \).

Perform the Calculation

Calculate the echo travel time: \( \text{echo travel time} = \frac{21,988}{1500} \approx 14.66 \, \text{seconds} \).

Key concepts

Depth Measurement in Oceans

Measuring depth in oceans is crucial for navigation, studying marine life, and understanding geological features. One common tool used for this purpose is the echo sounder. An echo sounder sends sound waves from a ship to the ocean floor and then measures the time it takes for the echo to return. By knowing the return trip time and the speed of sound in water, we can calculate the depth.

The formula used in depth measurement is:

• Depth = \( \frac{1}{2} \times \text{Speed of Sound in Water} \times \text{Echo Travel Time} \)

The division by two accounts for the sound travelling to the ocean floor and back. In our example, using a depth of 10,994 meters, we calculate the round trip time to measure how deep the ocean is at that point.

This process is vital for safe maritime navigation, helping ships avoid obstructive underwater features.

Speed of Sound in Water

The speed of sound in water is typically about 1500 meters per second. This rate can slightly vary depending on factors such as temperature, salinity, and pressure.

While in air the speed of sound is approximately 343 meters per second, water speeds are much higher due to the medium's density and elasticity. These properties allow sound waves to travel faster, which is advantageous in applications requiring precise measurements, like echo sounding.

Understanding how sound travels in water is essential in oceanography because it helps scientists and navigators accurately determine distances and detect objects underwater.

The Role of Oceanography in Depth Measurement

Oceanography is the scientific study of the ocean and includes examining physical, chemical, biological, and geological aspects. Measuring depth is a critical component in this field.

Oceanographers use tools like echo sounders to explore underwater landscapes and collect data that can reveal much about ocean processes and habitats. Accurate depth measurements can show changes in the seabed, such as those from tectonic activity or sediment deposition.

By better understanding the structure and form of the ocean floor, oceanography supports not only scientific research but also practical applications like resource extraction and environmental conservation.