Question

Assume that after seeing a lightning bolt you heard thunder 10 seconds later. About how far away did the lightning occur?

Short answer

The lightning occurred approximately 3.43 kilometers away.

Step-by-step solution

Understanding the Relationship

Light travels much faster than sound, so when you see lightning and then hear thunder after a delay, the sound has taken time to travel from the lightning to you. The speed of sound is approximately 343 meters per second (m/s) in air.

Calculating the Distance

Using the formula for distance: \[ ext{Distance} = ext{Speed} imes ext{Time} \]Substitute the values: speed of sound as 343 m/s and time as 10 seconds to find the distance as follows: \[ ext{Distance} = 343 ext{ m/s} imes 10 ext{ s} = 3430 ext{ meters}\]

Converting Meters to Kilometers

Since distances are often measured in kilometers for practical purposes, convert the distance from meters to kilometers by dividing by 1000:\[ ext{Distance} = \frac{3430 ext{ meters}}{1000} = 3.43 ext{ kilometers}\]

Key concepts

Speed of Sound

The speed of sound is a fascinating topic as it helps us understand how sound travels through different mediums. In the air, under standard conditions, sound travels at about 343 meters per second (m/s). This means that every second, sound covers a distance of 343 meters. The speed of sound can vary based on factors such as:

• Temperature: Sound travels faster in warmer air because the molecules are more active and facilitate quicker movement of sound waves.
• Pressure: Higher pressure means molecules are closer together, slightly enhancing sound speed.
• Medium: Sound travels faster through solids and liquids compared to gases like air due to denser molecular structure.

Understanding the speed of sound is crucial for calculating distances in various activities, such as determining how far away lightning has struck.

Distance Calculation

When calculating the distance of a lightning strike based on the sound of thunder, we use the relationship between speed, distance, and time. This is expressed in the formula:\[ \text{Distance} = \text{Speed} \times \text{Time} \]The process involves:

• Observing the time interval between seeing the lightning and hearing the thunder.
• Using the speed of sound in air, which is approximately 343 m/s.
• Multiplying the speed by the observed time delay to find the distance.

For example, if the delay is 10 seconds, the calculation will be:\[ \text{Distance} = 343 \, \text{m/s} \times 10 \, \text{s} = 3430 \, \text{meters} \]Finally, convert the distance from meters to kilometers for practical understanding by dividing by 1000:\[ \text{Distance} = \frac{3430 \, \text{meters}}{1000} = 3.43 \, \text{kilometers} \]

Lightning Safety

Being aware of lightning safety is crucial during storms. The ability to calculate the distance of a lightning strike can contribute to your safety management in severe weather conditions. Here are essential safety tips:

• When you see lightning and hear thunder, use the 30-30 rule: go indoors if there are less than 30 seconds between lightning and thunder, and stay indoors for 30 minutes after the last thunder sound.
• Avoid open fields, hilltops, or other elevated areas where strikes are more likely to occur.
• Stay away from trees and objects that can act as lightning conductors, including metal objects.
• Once inside, steer clear from windows, doors, and any electrical wiring.
• Remember that lightning can strike up to 10 miles away from a storm in an area called "the bolt from the blue."

By understanding and applying these safety principles, you can greatly reduce the risk of lightning-related injuries.