Respuesta :
ANSWER
343.5 m
EXPLANATION
Given:
• The time it takes the echo to return, t = 2s
,• The temperature of the air, T = 21°C
We have to find the distance to the lake.
If we have the speed of sound, s, the distance to the lake, d, is traveled twice by the sound - to the lake and back. Thus, the speed is,
[tex]s=\frac{2d}{t}[/tex]Solving for d,
[tex]d=\frac{s\cdot t}{2}[/tex]We don't know the speed of sound, but we know the temperature of the air. The speed of sound is given by,
[tex]s=331m/s\cdot\sqrt[]{\frac{T}{273K}}[/tex]Where T is the temperature in Kelvin. Transform the given temperature from degrees Celsius to Kelvin,
[tex]T=21+273=294K[/tex]The speed of sound at this temperature is,
[tex]s=331m/s\cdot\sqrt[]{\frac{294K}{273K}}\approx343.5m/s[/tex]And the distance to the lake is then,
[tex]d=\frac{343.5m/s\cdot2s}{2}=343.5m[/tex]Hence, the distance to the lake is 343.5 m.
