Question

Expert help me

Try to solve the following problems

•Compute the speed of sound in air at 25 0C. How long will this sound wave take to reach 1.5 km? If this sound wave propagates for 10 seconds more, what will be the total distance traveled?
•At what temperature can the sound travel at 345 m/s?​​

Answer 1

346 m/s

4.34 s (2 d.p.)

4960 m

23.33 °C (2 d.p.)

Step-by-step explanation:

Speed of sound in air

`\boxed{v=331+0.6T}`

Where:

• v = velocity in m/s
• T = temperature in °C

Substitute the given temperature of 25°C into the formula and solve for v:

`\implies v=\sf331+0.6(25)=346\; m/s`

As 1 km = 1000 m then:

⇒ 1.5 km = 1500 m

`\boxed{\sf Time=(Distance)/(Speed)}`

Substitute the distance of 1500 m and the speed of 346 m/s into the formula and solve for time:

`\implies \sf Time=(1500)/(346)=4.34\;s\;(2\:d.p.)`

`\boxed{\sf Distance=Speed * Time}`

10 seconds more would be:

`\implies \sf (1500)/(346)+10=14.33526012...`

Substitute the speed of 346 m/s and the time into the formula and solve for distance:

`\begin{aligned}\implies \sf Distance &= \sf Speed * Time\\&= \sf 346 * 14.33526012...\\&=\sf 4960\;m \end{aligned}`

To calculate what temperature the sound can travel at 345 m/s, substitute this speed into the Speed of sound in air formula and solve for T:

`\begin{aligned} v&=331+0.6T\\\implies 345 & = 331+0.6T\\345 -331& = 331+0.6T-331\\14&=0.6T\\T&=(14)/(0.6)\\\implies T&=23.33^(\circ)\sf C\end{aligned}`