A man standing 2040m from the foot of a high building claps his hands and hears the echo. 4 second later (speed of sound in air at 0 ^ 0 * c is 331m / s )
a. What is the velocity of the sound in the air?
b. What is the temperature at that place?
a. We can use the formula:
distance = speed x time
The man claps his hands and hears the echo 4 seconds later. This means the sound had to travel a total of 4080 meters (2040m to the building and then back to the man). So:
4080m = speed x 4s
Speed = 1020 m/s
Therefore, the velocity of the sound in the air is 1020 m/s.
b. The speed of sound in air depends on the temperature of the air. At 0 ^ 0 *C, the speed of sound in air is 331 m/s. We can use the formula:
speed = 331 m/s x sqrt(1 + (T/273))
where T is the temperature in degrees Celsius.
We can rearrange this formula to solve for T:
T = (speed/331)^2 x 273 - 273
Plugging in the speed we found above, we get:
T = ((1020 m/s)/331)^2 x 273 - 273
T ≈ 39°C
Therefore, the temperature at that place is approximately 39°C.
To solve this problem, we can use the formula:
Velocity = Distance / Time
a. To find the velocity of sound in the air, we can calculate the total distance covered by the sound. The man claps his hands and hears the echo after 4 seconds, which means the sound traveled a distance of 2040m to reach the building and another 2040m to return.
Total distance = 2040m + 2040m = 4080m
Using the formula, Velocity = Distance / Time, we can calculate the velocity:
Velocity = 4080m / 4s
Velocity = 1020 m/s
Therefore, the velocity of sound in the air at that location is 1020 m/s.
b. To find the temperature at the location, we can use the relationship between temperature and the speed of sound:
Speed of sound = 331 m/s + 0.6 m/s/°C * Temperature
Rearranging the formula, we can solve for the temperature:
Temperature = (Speed of sound - 331 m/s) / 0.6 m/s/°C
Temperature = (1020 m/s - 331 m/s) / 0.6 m/s/°C
Temperature = 681 m/s / 0.6 m/s/°C
Temperature ≈ 1135 °C
Therefore, the estimated temperature at that place is approximately 1135 °C.