Two friends A and B are
standing a distance x apart in an
open field and wind is blowing from A to
B.
A beats a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum t2 time after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
The beats are a unit of time.
t = d/v
In the first experiment, the wind is assisting the speed of sound. The total speed is v + u. Therefore the time = x / (v + u)
11 = x / (v + u)
11v + 11u = x
In the second experiment, the wind is going against the travel of direction. v - u
The equation you get is
12v - 12u = x
The two x's are an equal distance So you can begin by equating the two distances.
12v - 12u = 11v + 11u
v = 23 u
Now you can go to one of the original equations.
12v - 12u = x
12*23u - 12u = x
12u (23 - 1) = x
12u * 22 = x
u = x / 264
v = 23*u
v = 23 * x/264
A beats a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum t2 time after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
The beats are a unit of time.
t = d/v
In the first experiment, the wind is assisting the speed of sound. The total speed is v + u. Therefore the time = x / (v + u)
11 = x / (v + u)
11v + 11u = x
In the second experiment, the wind is going against the travel of direction. v - u
The equation you get is
12v - 12u = x
The two x's are an equal distance So you can begin by equating the two distances.
12v - 12u = 11v + 11u
v = 23 u
Now you can go to one of the original equations.
12v - 12u = x
12*23u - 12u = x
12u (23 - 1) = x
12u * 22 = x
u = x / 264
v = 23*u
v = 23 * x/264
Answer: In the first case resultant velocity = u+v
So the time taken t1 = x/(u+v)
→ u+v = x/t1 ..................(A)
In the second case resultant velocity = v-u
Now the time taken = t2 = x/(v-u)
→ v-u = x/t2 ................(B)
Adding the equations (A) and (B)
2 v = x/t1 + x/t2
→ v = x/2 * (1/t1+1/t2) It is the velocity of sound in still air.
Subtracting (B) and (A) we get
2u = x/t1 - x/t2
→ u = x/2 * (1/t1 - 1/t2) It is the velocity of wind .
the velocity of sound and wind are added vectorially.
therefore, in the first case,
v + u = x/t1 ........................ (1)
v - u = x/t2 ...........................(2)
on adding, we get
v = x (1/t1 + 1/t2) / 2
on subtracting,
u = x (1/t1 - 1/t2) / 2
in the second case,
the resultant velocity and u are at 900 to each other
therefore,if u make a rt. triangle,
v acts as hypotenuse and u as a leg and resultant vel. towards B makes the other leg. therefore,
Resultant vel. =
v2 - u2
time taken = x
v2 - u2
therefore, in the first case,
v + u = x/t1 ........................ (1)
v - u = x/t2 ...........................(2)
on adding, we get
v = x (1/t1 + 1/t2) / 2
on subtracting,
u = x (1/t1 - 1/t2) / 2
in the second case,
the resultant velocity and u are at 900 to each other
therefore,if u make a rt. triangle,
v acts as hypotenuse and u as a leg and resultant vel. towards B makes the other leg. therefore,
Resultant vel. =
v2 - u2 time taken = x
v2 - u2 
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