Question

If you are 600 m from a batter when you see him hit a ball, how long will you wait to hear the sound of the bat hitting the ball? (at 20ºC)?

Speed of sound at 20ºC =?
time =?

Answer 1

The speed of sound at 20°C is 343.42 m/s.

You have to wait 1.75 seconds to hear the sound of the bat hitting the ball

Explanation:

Speed of Sound

The speed of sound is not constant with temperature. Generally speaking, the greater the temperature, the greater the speed of sound.

The approximate speed of sound in dry air at temperatures T near 0°C is calculated from:

`\displaystyle v_{\mathrm {s} }=(331.3+0.606\cdot T )~~~\mathrm {m/s}`

The air is at T=20°C, thus the speed of sound is:

`\displaystyle v_{\mathrm {s} }=(331.3+0.606\cdot 20 )~~~\mathrm {m/s}`

`v_{\mathrm {s} }=343.42\ m/s`

The speed of sound at 20°C is 343.42 m/s.

To calculate the time to hear the sound after the batter hits the ball, we use the formula of constant speed motion:

`\displaystyle v=(d)/(t)`

Where d is the distance and t is the time. Solving for t:

`\displaystyle t=(d)/(v)`

Substituting the values v=343.42 m/s and d=600 m:

`\displaystyle t=(600)/(343.42)`

t = 1.75 s

You have to wait 1.75 seconds to hear the sound of the bat hitting the ball