Question

Assuming that the average speed of sound waves in water is 1500 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 4500 meters.

Step-by-step solution

Understand the Problem

We want to find the water depth given that an echo sounder takes 6 seconds for the signal to travel to the bottom of the water and back. The speed of sound in water is provided as 1500 meters per second.

Determine the Total Travel Time

The total travel time for the sound wave to travel to the bottom and return is given as 6 seconds. This includes both going to the bottom and coming back to the surface.

Calculate the One-Way Time

Since the total travel time is for the round trip (down and up), we divide the total time by 2 to find the time taken to reach just the bottom. \[ \text{One-way time} = \frac{6}{2} = 3 \text{ seconds} \]

Use the Speed Equation to Determine Depth

We use the formula \( \text{distance} = \text{speed} \times \text{time} \). Here, the time is for one-way travel (3 seconds) and the speed is 1500 m/s:\[ \text{Depth} = 1500 \text{ m/s} \times 3 \text{ s} = 4500 \text{ meters} \]

Review and Conclude

Verify that the interpretation of the echo sounder problem is correct and ensure calculations were performed accurately. The depth found is 4500 meters.

Key concepts

Echo Sounder

An echo sounder, often used in maritime and underwater research, is a scientific instrument essential for measuring water depths. It works by emitting sound pulses directly into the water. When these sound waves hit an object, such as the sea floor, they bounce back to the echo sounder. This reflected sound wave is called an echo, hence the name "echo sounder."

Echo sounders provide critical data for mapping ocean terrains and ensuring safe navigation. They help scientists understand oceanographic features and play a significant role in underwater exploration. This device can be mounted on ships, making it versatile for various oceanic and lake environments.

Speed of Sound

The speed of sound is the rate at which sound waves travel through a medium. In water, the speed of sound is significantly faster than in air, averaging around 1500 meters per second. This speed can vary based on factors such as water temperature, salinity, and depth.

Understanding the speed of sound in water is key for accurately calculating distances using an echo sounder. This constant speed allows for precise depth calculations that are crucial for scientific, commercial, and navigational activities.

Water Depth Calculation

Calculating water depth using sound involves straightforward physics. By knowing the speed of sound in water and measuring the time it takes for sound waves to travel to the seafloor and back, the water depth can be determined.

• First, use the formula for distance: \[ \text{distance} = \text{speed} \times \text{time} \]
• Since the echo travels to the bottom and back, divide the total time in half to find the one-way travel time.
• Multiply this time by the speed of sound to get the depth.

For example, if the total round-trip time is 6 seconds and the speed is 1500 m/s, the calculation is: \[ \text{Depth} = 1500 \text{ m/s} \times 3 \text{ s} = 4500 \text{ meters} \]
Thus, the depth of the water is concluded to be 4500 meters.

Physics of Sound Waves

Sound waves are a type of mechanical wave known as longitudinal waves, traveling through mediums like air or water by compressing and decompressing particles.

In water, sound waves travel faster and more efficiently due to the medium's density and elasticity. This propagation involves the waves transferring energy through molecular interactions, a process that is pivotal in echo sounding.

Understanding the physics of sound waves allows scientists to use sound waves to gather detailed information about underwater environments, revealing insights that are difficult to gain by other methods. These waves are fundamental to numerous applications beyond echo sounding, including sonar and underwater communication systems.