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

Speed of sound in air;

- From temperature dependence of sound speed;

`{ \rm{velocity = 331 \sqrt{1 + ( \theta)/(273.16) } }} \\ \\ { \rm{ = 331 \sqrt{1 + (25)/(273.16) } }} \\ \\ = { \rm{345.8 \: {ms}^( - 1) }}`

Time taken by the wave through 1.5 km;

`{ \tt{time = (distance)/(speed) }} \\ \\ { \tt{time = (1.5 * 1000)/(345.8) }} \\ \\ { \tt{time = 4.34 \: seconds}}`

Distance in supplement of 10 seconds;

`{ \tt{distance = (t _(1) + t _(2)) * speed}} \\ { \tt{d = (4.34 + 10) * 345.8}} \\ { \tt{d = 49587.72 \: m}} \\ { \tt{d =49.58 \: km }}`

Temperature for sound to travel at 345 m/s

`{ \tt{v = 331 \sqrt{1 + ( \theta)/(273.16) } }} \\ \\ { \tt{ 345 = 331 \sqrt{1 + ( \theta)/(273.16) } }} \\ \\ { \tt{ \theta = 23.6 \degree c}} \\ { \tt{temperature = 23.6 \degree c}}`