Question

The speed of sound in air at room temperature is about \(343 \mathrm{~m} / \mathrm{s}\). Calculate this speed in miles per hour \((1 \mathrm{mi}=1609 \mathrm{~m})\).

Short answer

The speed of sound is approximately 768 mph.

Step-by-step solution

Understand the Problem

We are given the speed of sound in air as 343 meters per second and need to convert this speed to miles per hour.

Convert Meters to Miles

To convert meters to miles, use the conversion factor: \(1 \text{ mile} = 1609 \text{ meters}\). The speed in miles per second is calculated as: \[\text{Speed in mph} = \frac{343 \text{ meters/second}}{1609 \text{ meters/mile}}\].

Perform the Conversion

Calculate the speed in miles per second using the conversion factor: \[\text{Speed in miles/second} = \frac{343}{1609} \approx 0.213 \text{ miles/second}\].

Convert Miles per Second to Miles per Hour

Since there are 3600 seconds in an hour, multiply the speed in miles per second by 3600 to convert to miles per hour: \[\text{Speed in mph} = 0.213 \text{ miles/second} \times 3600 \text{ seconds/hour} \approx 768 \text{ mph}\].

Verify the Calculation

Re-check each step and ensure unit conversions and calculations are correct. Confirming the speed of sound is approximately 768 mph.

Key concepts

sound speed conversion

Converting units of speed involves changing one measurement into an equivalent value in a different unit system. When dealing with the speed of sound, which is about 343 meters per second at room temperature, the process involves transforming meters to miles and seconds to hours.
This conversion is essential because speeds are often expressed in miles per hour (mph) in countries like the United States, where the imperial system is used. To convert the speed of sound to miles per hour, we first determine how many miles correspond to a certain number of meters, and then adjust for the time from seconds to hours.
Understanding these conversions makes it easier to compare and understand different speed measures across various systems of measurement, providing a universal understanding of rates, such as the speed at which sound travels.

meters to miles

Converting meters to miles is a straightforward unit conversion commonly needed in science and everyday contexts. A mile is a longer unit than a meter, with one mile equating to 1609 meters. To find out how a certain number of meters translates into miles, you divide the number of meters by 1609.
For example, to convert 343 meters to miles, you use the formula:

• Speed in miles per second = \(\frac{343 \text{ meters}}{1609 \text{ meters/mile}} \)
• Calculating gives approximately 0.213 miles per second

This fundamental conversion factor is critical for accurately translating measurements in science, engineering, and travel, especially when translating metrics to the more US-favored imperial system. It helps to know this conversion factor and apply it correctly in all contexts, allowing consistency in unit conversions.

miles per hour conversion

Miles per hour is a common unit of speed often used in road speed limits and vehicle speedometers. To convert a speed measured in a small unit of time like seconds into an hourly rate, understanding the time conversion is key. There are 3600 seconds in one hour, which means any measurement in miles per second must be multiplied by 3600 to determine the speed in miles per hour.
This process for our speed of sound example involves taking the speed in miles per second (0.213 miles/second for sound) and multiplying:

• Miles per hour = \(0.213 \text{ miles/second} \times 3600 \text{ seconds/hour}\)
• The resulting speed is approximately 768 mph

This conversion is vital for understanding speeds on a scale that relates more closely to human experience and common measuring systems. It ensures that the amazing speed of phenomena like sound or vehicles can be expressed in relatable terms.