Question

Assuming the average speed of sound waves in water is 1,500 meters per second, determine the water depth if a signal sent out by an echo sounder on a research vessel requires 6 seconds to strike bottom and return to the recorder aboard the ship.

Short answer

The water depth is 4,500 meters.

Step-by-step solution

Understand the problem

We are given that the speed of sound in water is 1,500 m/s and that the total time for the sound to travel to the bottom and back is 6 seconds. We need to find the depth of the water, which is the one-way distance to the bottom.

Determine the total distance traveled

Sound travels to the bottom and back up, so the time given is for the round trip. Therefore, we need to calculate the total distance using the formula: \[ \text{Total Distance} = \text{Speed} \times \text{Time} \]. Plugging in the values, we get: \[ \text{Total Distance} = 1,500 \text{ m/s} \times 6 \text{ s} = 9,000 \text{ meters} \].

Calculate the one-way distance (depth)

Since the total distance is for a round trip, we need to find the one-way distance by dividing the total distance by 2: \[ \text{Depth} = \frac{\text{Total Distance}}{2} = \frac{9,000 \text{ meters}}{2} = 4,500 \text{ meters} \].

Key concepts

Echo Sounder

An echo sounder is a remarkable piece of technology used to measure the depth of water beneath a ship. It functions by emitting sound waves from the ship's hull into the water. These waves travel through the water until they hit the seabed. Upon reaching the bottom, they bounce back up to the surface, where they are detected by the echo sounder.

Echo sounders are valuable tools for navigators and scientists alike. They help in charting the seafloor, indicating safe routes, and ensuring ships avoid underwater obstacles.

• Originally invented in the early 20th century, echo sounders have evolved significantly with improved precision and technology.
• They are commonly used in both civilian and military maritime operations.
• The speed of sound in water, assumed here to be 1,500 meters per second, is crucial for calculating the depth accurately.

Understanding how an echo sounder works is fundamental to comprehending how sound waves interact with water and how depth measurements are derived.

Water Depth Calculation

Calculating the depth of water using an echo sounder revolves around the simple relationship between speed, distance, and time. With an echo sounder, the depth calculation follows a logical sequence:

The sound wave emitted by the echo sounder travels to the seabed and returns to the ship. This two-way journey time is crucial: it's essentially a round-trip.

• To calculate the total distance the sound wave travels, use the formula: \( \text{Total Distance} = \text{Speed} \times \text{Time} \).
• In our case, with a speed of 1,500 meters per second and a 6-second round trip time, the total distance is 9,000 meters.

However, to determine just the one-way distance—the true depth of the water—we need to divide this total distance by two. This results in a water depth of 4,500 meters. Each part of the calculation is straightforward, but accuracy is crucial in each step to ensure reliable depth measurements.

Speed of Sound in Water

The speed of sound in water is a vital parameter when using echo sounders or engaging in any aquatic acoustics activities. It is generally accepted that sound travels faster in water than in air. This is due to the density and properties of water, which facilitate the rapid passage of sound waves.

At standard conditions, the speed of sound in water is about 1,500 meters per second. However, several factors can influence this speed:

• **Temperature**: Warmer waters tend to increase sound speed.
• **Salinity**: Higher salt content usually raises the speed, as more ions in solution strengthen the medium.
• **Pressure**: Greater depths result in higher pressures, which in turn enhance sound velocity.

These factors combine to create environments where the sound speed may vary. For tasks such as depth sounding or sonar applications, knowing the actual speed of sound in water at the specific location is crucial for precision. Calculating a consistent average speed ensures that depth readings remain accurate, even with environmental variations.