Solve Airplane Sound Wave Problem: Speed & Altitude

[the_storm]

Homework Statement

The speed of the sound in the air (in meter per second) depends on temperature according to approximate expression
V= 313.5 + 0.607T_c
where T_c is the Celsius temperature. In dry air, the temperature decreases about 1 degree Celsius for every 150M rise in altitude

Homework Equations

a) assume the change is constant up to an altitude of 9000m what time interval is required for the sound from airplane flying at 9000m to reach the ground on a day when the ground temperature is 30 Celsius

 

[aim1732]

Please show some work.

 

[the_storm]

I have tried to make integration because the velocity is changing
I said that T =$$\frac{x}{v}$$ >>
x = 9000 m
v = $$\int(313.5+0.607t)dt$$ and the limit of integration fro, -30 to 30
but it doesn't work

 

[hikaru1221]

I'm not sure what you mean by dv=vdt (deduced from your integral). Anyway, here is the way:
1 - We have dt = dx/v
2 - As v is given depending on T (note: t and T are different, one is time, the other is temperature), and we also have the variation law of T versus x (x is also height), we can derive v versus x.
Then, it's just simple math