Chapter 6: Problem 17

In the past, ships often carried small cannons that were used when approaching shore in dense fog to estimate the distance to the hidden land. Explain how this might have been done.

Short Answer

Expert verified

Answer: Ships in the past might have used small cannons to estimate the distance to the hidden land by firing the cannon and measuring the time it took for the sound to travel to the shore and bounce back to the ship. By using the speed of sound and the measured time, sailors could calculate the distance from the ship to the shore using the formula: Distance = (Speed of sound) * (Time) / 2. However, this method has some limitations, such as variations in the speed of sound due to temperature, humidity, and air pressure, the potential for inaccurate time measurements, and the possibility of sound bouncing off other objects before reaching the shore.

Step by step solution

Understand the concept of speed of sound

Sound travels through the air at a constant speed, which depends on the temperature and humidity of the air. On average, the speed of sound is approximately 343 meters per second (m/s) at sea level and a temperature of 20 degrees Celsius. This information will be useful when we discuss how the time it takes for the cannon's sound to reach the shore and bounce back to the ship can be used to calculate the distance to the hidden land.

Calculate the time it takes for the sound to travel

When a cannon is fired, its sound travels through the air at the speed of sound. In this case, the cannon's sound will travel to the shore, bounce off the land, and travel back to the ship. To calculate the time it takes for this entire process to occur, we would start by measuring the time from when the cannon is fired to when its sound returns to the ship.

Use the speed of sound and time to estimate the distance

Once we have the time it takes for the cannon's sound to travel to the shore and back to the ship, we can use the speed of sound to estimate the distance to the hidden land. To do this, we can use the formula: Distance = (Speed of sound) * (Time) / 2 The reason we divide the time by 2 is that we want to find the one-way distance to the shore, not the round-trip distance. Using the average speed of sound (343 m/s) and the measured time, we would calculate the distance from the ship to the shore.

Understand the limitations and possible errors

It's important to note that this method of estimating the distance to land has some limitations and possible sources of error. Firstly, the speed of sound can vary depending on factors such as temperature, humidity, and air pressure, which can lead to inaccuracies in the distance calculation. Secondly, the time it takes for the cannon's sound to travel might be difficult to measure accurately, particularly if the fog is very dense. Additionally, the sound may bounce off other objects in the water (like other ships or floating debris) before reaching the shore, which could further complicate the calculation. Despite these limitations, using small cannons to estimate the distance to the hidden land was a clever method employed by ships in the past when approaching shore in dense fog. By understanding the speed of sound and carefully measuring the time it took for the cannon's sound to return, sailors could make reasonably accurate estimations of their proximity to land.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance Estimation in Fog

Navigating through fog can be a daunting challenge due to the severe reduction in visibility. In historical times, sailors used the sound of cannons to estimate the distance to the shore, a technique rooted in the principles of sound travel. When a cannon was fired, sailors would time the echo reflected off the landmass and use this to gauge their location relative to the shore. This method assumes that the sound travels at a steady pace through the medium of air. However, factors such as fog density can influence the propagation of sound and, therefore, the accuracy of the distance estimation. Despite potential errors, this rudimentary form of acoustic ranging proved invaluable in preventing ships from running aground in poor visibility conditions.

Speed of Sound

The speed of sound, approximately 343 meters per second at 20 degrees Celsius at sea level, is a critical value for various navigational and scientific calculations. It is essential to understand that this speed is not constant but varies with changes in air temperature, humidity, and pressure. For example, in colder conditions, the speed of sound decreases, as sound waves travel more slowly through denser air. It's important for students to grasp that while the average speed of sound provides a starting point for calculations, environmental conditions must be taken into account to achieve precise results, especially when employing these calculations for practical purposes like distance estimation in fog.

Sound Travel Time Measurement

The measurement of how long it takes for sound to travel a certain distance is a fundamental aspect of acoustic ranging. The timing begins the moment the sound is produced, such as the firing of a cannon, and stops when the echo is detected. To calculate the distance, the total travel time is then analyzed using the known speed of sound. However, timing this accurately can be challenging without modern instrumentation. In historical practices, precision was limited to the sailor's reaction time and the quality of their time-keeping devices, which could lead to significant measurement errors. Regardless, this practice of timing sound travel provided a basic yet functional method for sailors to measure their proximity to obstacles or land.

Acoustic Ranging

Acoustic ranging is a technique that uses the travel time of sound to measure distance. It is not just historical curiosity but the foundation of modern technologies such as sonar and ultrasound. Acoustic waves are directed toward an object, and their echoes, once returned, are analyzed to determine how far away that object is. When projectiles like cannonballs were used, the blast provided an audible signal used to trigger the start of timing. The sound wave would travel to the shore, reflect off it, and return to the ship, where the timing would stop. The time recorded is the round-trip time, hence it's divided by two to get the one-way distance. While this method's efficacy can be impaired by various factors like temperature variations and reflective interference, it still embodies the basic principles used in distance measurement by sound, which remain relevant to numerous applications today.

In the past, ships often carried small cannons that were used when approaching shore in dense fog to estimate the distance to the hidden land. Explain how this might have been done.

Short Answer

Step by step solution

Understand the concept of speed of sound

Calculate the time it takes for the sound to travel

Use the speed of sound and time to estimate the distance

Understand the limitations and possible errors

Key Concepts

Distance Estimation in Fog

Speed of Sound

Sound Travel Time Measurement

Acoustic Ranging

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