Question

The speed of sound in air at room temperature is about \(343 \mathrm{~m} / \mathrm{s}\). Calculate this speed in miles per hour \((\mathrm{mph})\)

Short answer

The speed of sound in air at room temperature is approximately 767.62 mph.

Step-by-step solution

Understand the Conversion Rates

Before starting the conversion, it's important to note the conversion rates from the metric system to the imperial system. One mile is approximately equal to 1609.34 meters and one hour is equal to 3600 seconds.

Convert Meters to Miles

The speed of sound given is 343 m/s. To convert meters to miles, divide 343 by the conversion factor of 1609.34 meters/mile. This gives \( \frac{343}{1609.34} = 0.213 miles/sec \).

Convert Seconds to Hours

Now, to convert the time from seconds to hours, multiply the above value by the conversion factor of 3600 seconds/hour. This gives \(0.213 miles/sec × 3600 sec/hour = 767.62 mph\) (rounded to two decimal places).

Key concepts

Converting Metric to Imperial Units

Understanding the conversion between metric to imperial units is vital for many scientific calculations and daily life applications. The metric system, which includes meters, kilograms, and seconds, is commonly used in science and many parts of the world for measuring distance, mass, and time. On the other hand, the imperial system, which uses units such as miles, pounds, and hours, is used mainly in the United States.

When faced with the need to convert metric units to imperial units, it's essential to know the basic equivalences. For example, knowing that one mile is equal to 1609.34 meters is crucial when converting measurements of distance from metric to imperial. Similarly, to convert time, you should remember that one hour contains 3600 seconds. Keeping a conversion chart or calculator handy can simplify these conversions.

Simple Conversion Tips

• To convert meters into miles, divide the number of meters by 1609.34.
• To convert seconds into hours, divide the number of seconds by 3600.

Memorizing or having these rates accessible can significantly streamline the process of converting units across different systems, helping you solve problems like calculating the speed of sound in various units.

Calculating Speed of Sound

The speed of sound varies depending on the medium through which it travels, and it is a fundamental concept in physics. At room temperature, which is approximately 20 degrees Celsius or 68 degrees Fahrenheit, sound travels through air at about 343 meters per second (m/s). Nevertheless, this can change with temperature, altitude, and the nature of the medium.

To calculate the speed of sound, or to convert it into different units, it's essential to start with a known value. In the context of the original problem, the starting point is the speed of sound in air at room temperature given as 343 m/s. This value is then converted to other units, like miles per hour (mph), based on conversion factors between metric and imperial units.

Factors Affecting the Speed of Sound

• Temperature: Sound travels faster in warmer conditions.
• Medium: Sound speed is different in air, water, and solids.
• Altitude: The speed of sound decreases with an increase in altitude.

Grasping these principles and their mathematical applications enables us to understand sonic phenomena, such as sonic booms and the Doppler effect, and how they are perceived under varying conditions.

Units of Measurement Conversion

Unit conversion is a core skill in various fields including science, engineering, and everyday life. The process involves converting a measurement expressed in one set of units to another set of units, often using a conversion factor or equation. For instance, when we convert from metric to imperial units or vice versa, we are translating the measure of a physical quantity from one system to another.

These conversions are not arbitrary; they rely on well-defined equivalences. For speed, converting from meters per second (m/s) to miles per hour (mph) involves two main steps: converting the measure of distance and the measure of time. Once you understand the foundational conversion rates — such as how many meters are in a mile or how many seconds in an hour — you can apply these to convert any measure of physical quantities.

Why Accurate Conversion Matters

• Provides consistency and standardization in measurements.
• Ensures accuracy in scientific calculations and communications.
• Enables comparison and compatibility in international trade and relations.

Through conscientious conversions, we can maintain the integrity of data, understand global concepts, and ensure that structures like buildings and vehicles are designed safely and efficiently.