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 $=1/2(1500\mathrm{m}/\sec \times$ echo travel time).

Short answer

It takes approximately 14.66 seconds for the echo to make the round trip.

Step-by-step solution

Understand the Formula

First, recall the formula for calculating depth using an echo sounder: $\text{Depth}=\frac{1}{2}\times \text{Speed of sound in water}\times \text{Echo travel time}$. The speed of sound in water is given as 1500 m/s.

Rearrange the Formula for Time

Since we need to find the echo travel time, rearrange the formula to solve for time. The formula becomes: $\text{Echo travel time}=\frac{2\times \text{Depth}}{\text{Speed of sound in water}}$.

Plug in Known Values

We know the depth to the Challenger Deep is 10,994 meters and the speed of sound is 1500 m/s. Substitute these values into the equation: $\text{Echo travel time}=\frac{2\times 10,994}{1500}$.

Perform the Calculation

Calculate the echo travel time: $\text{Echo travel time}=\frac{21,988}{1500}=14.66$ seconds approximately.

Key concepts

Challenger Deep

Challenger Deep is the deepest known point in the Earth's seabed. Located in the Mariana Trench, it reaches a depth of approximately 10,994 meters (about 36,070 feet). This extreme depth makes it a point of great interest for researchers studying marine geology and biology. Exploration here is incredibly challenging due to the extreme pressure and darkness that exists at this depth. These explorations often rely on technology such as submersibles and sophisticated sonar systems known as echo sounders, which help in mapping and studying the trench. Studying such depths can provide valuable information about Earth's geological history and life forms that exist in such difficult conditions.

Speed of Sound in Water

The speed of sound is considerably faster in water than in air. In water, sound travels at about 1500 meters per second (m/s), depending on several factors.

• Temperature: Warmer water can increase the speed.
• Salinity: Higher salinity can also increase speed.
• Pressure: Greater depth and pressure can affect speed as well.

Understanding the speed of sound in water is crucial for applications like sonar technology, which is used extensively in marine research, navigation, and communication. This knowledge assists in accurately determining distances underwater by calculating how long it takes for sounds to travel to reflect off an object, like the ocean floor, and return.

Echo Travel Time

Echo travel time is a crucial component in underwater distance measurement. It refers to the time taken for a sound wave (ping) to travel from its source to a target and back. In the case of measuring ocean depth, the target is typically the seafloor.To calculate echo travel time, one uses the formula:$$\text{Echo travel time}=\frac{2\times \text{Depth}}{\text{Speed of sound in water}}$$For the Challenger Deep, the formula helps determine how long it takes for the sound to travel to nearly 11,000 meters depth and back to the source. With a speed of 1500 m/s in water, calculating the echo travel time reveals how long it takes for sound reflections to complete this journey, providing essential data for accurately calculating ocean depth and facilitating underwater exploration.