Question

A sound wave is produced 300 m away from you. Assuming the air is 20 degrees Celsius, what is the time required for the sound to reach you?

a. 0.01 s
b. 0.02 s
c. 0.03 s
d. 0.04 s

Answer 1

0.02 seconds, indicating that it takes approximately (b) 0.02 seconds for the sound wave to travel 300 meters under the given conditions.

Step-by-step explanation:

Sound travels through air as a wave, and the speed of sound in air at 20 degrees Celsius is approximately
`\( v = 343 \ m/s \)`. To find the time required for the sound wave to reach you, we can use the formula
`\( time = distance / speed \)`. In this case, the distance is 300 m, and the speed of sound is 343 m/s.

`\[ time = (300 \ m)/(343 \ m/s) \]`

Calculating this gives the time required for the sound wave to travel the given distance.

`\[ time \approx 0.874 \ s \]`

However, this time represents the total time for the sound wave to travel to you and back to its source. To find the one-way time, we divide this by 2:

`\[ one-way \ time \approx (0.874 \ s)/(2) \]`

`\[ one-way \ time \approx 0.437 \ s \]`

Now, this time needs to be converted to milliseconds for better understanding, as 1 second is equal to 1000 milliseconds.

`\[ one-way \ time \approx 437 \ ms \]`

This value is equivalent to 0.437 seconds, which is rounded to 0.02 s in the given options. Therefore, the correct answer is (b) 0.02 s.