A splash is heard 3.12s after a stone is dropped into a well 45m deep.the speed of sound in air is(g=10m/s2)
The time when the stone reaches the ground =(45*2)/10=3 sec.so,time taken by sound = 3.12-3= 0.12 sec. Now distance travelled by sound is 45 m,time=0.12sec . Speed=distance/ time =45/0.12=375m/sec
To find the speed of sound in air, we can use the equation: speed = distance / time.
Given:
Depth of the well (h) = 45 m
Time taken for the sound to reach the top of the well (t) = 3.12 s
Acceleration due to gravity (g) = 10 m/s^2
Step 1: Calculate the time taken by the stone to reach the bottom of the well.
Using the equation: s = ut + (1/2)gt^2
Where:
s = distance (depth of the well)
u = initial velocity (0 m/s as the stone is dropped)
t = time taken
Plugging in the values:
45 = 0 + (1/2)(10)(t^2)
45 = 5t^2
9 = t^2
Taking the square root of both sides:
t = √9
t = 3 s
Step 2: Calculate the time taken by the sound to reach the top of the well.
The total time for the sound to reach the top is 3.12 seconds. Since the stone took 3 seconds to fall to the bottom, the sound took an additional time of 0.12 seconds to reach the top.
Step 3: Calculate the distance traveled by the sound.
Using the equation: distance = speed × time
Where:
distance = depth of the well
speed = unknown (let's call it v)
time = 0.12 seconds
Plugging in the values:
45 = v × 0.12
Solving for v:
v = 45 / 0.12
v ≈ 375 m/s
Therefore, the speed of sound in air is approximately 375 m/s.
To find the speed of sound in air, we can use the formula:
speed = distance / time
In this case, the distance is the depth of the well (45m) and the time is the time it takes for the sound to travel back up (3.12s). Since the sound travels down and back up, we need to divide the time by 2.
First, let's calculate the time it takes for the stone to fall to the bottom of the well. We can use the formula:
distance = 0.5 * g * t^2
where g is the acceleration due to gravity (10 m/s^2) and t is the time taken by the stone to fall.
Rearranging the formula, we get:
t = sqrt(2 * distance / g)
Plugging in the values, we have:
t = sqrt(2 * 45 / 10)
= sqrt(9)
= 3 seconds
Now, we know the stone took 3 seconds to reach the bottom of the well. Therefore, the sound took 3.12 - 3 = 0.12 seconds to travel back up.
Since the sound traveled up 45 meters in 0.12 seconds, we can now calculate the speed of sound using the formula mentioned earlier:
speed = distance / time
= 45 / 0.12
= 375 m/s
Therefore, the speed of sound in air is 375 m/s.
Let the speed of sound be s. Then the time taken for the splash to be heard is 45/s seconds.
That means that the stone fell for 3.12 - 45/s seconds.
You know that stone fell 45m, so
5(3.12-45/s)^2 = 45
s = 375 m/s
not too close to the expected value of 343 m/s...