Respuesta :
Given data:
Distance between the sound source and the ear of the listener: d = 1.2 km
Speed of sound in water: V(water) = 1498 m/s
To find:
Time difference between the speed of sound in air and the speed of sound in water.
Explanation:
The speed of sound in air at temperature T is given by:
[tex]V(air)=331+0.59T[/tex]Here, T is the temperature and V(air) is the speed of sound in air measured in m/s.
Substitute the given values in above equation, we get:
[tex]\begin{gathered} V(air)=331+0.59\times30 \\ V(air)=348.7\text{ m/s} \end{gathered}[/tex]Thus, the speed of sound in air at 30°C is 348.7 m/s.
The time is taken by sound in air to travel a distance of 1.2 km is:
[tex]t(air)=\frac{d}{V(air)}[/tex]Substitute the values and simplify the above equation, we get:
[tex]\begin{gathered} t(air)=\frac{1.2\text{ km}(\frac{1000\text{ m}}{\text{km}})}{348.7\text{ m/s}} \\ t(air)=\frac{1200\text{ m}}{348.7\text{ m/s}} \\ t(air)=3.44\text{ s} \end{gathered}[/tex]Thus, the time taken by sound to travel in air is 3.44 seconds.
Now the speed of sound in water is given. The time taken by sound to travel a distance of 1.2 km in water is:
[tex]t(water)=\frac{d}{V(water)}[/tex]Substitute the values and simplify the above equation, we get:
[tex]\begin{gathered} t(water)=\frac{1.2\text{ km}\lbrack(\frac{1000\text{ m}}{\text{km}})}{1498\text{ m/s}} \\ t(water)=\frac{1200\text{ m}}{1498\text{ m/s}} \\ t(water)=0.80\text{ s} \end{gathered}[/tex]The time taken by sound to travel through water is 0.80 seconds.
The time difference between the speed of sound in air and speed of sound in water is:
[tex]\begin{gathered} t=t(air)-t(water) \\ t=3.44\text{ s }-0.80\text{ s} \\ t=2.64\text{ s} \end{gathered}[/tex]Final answer:
The difference between the time taken by sound to travel in air and the time taken by sound to travel in water is 2.64 seconds.
