The speed of sound in air is approximately 340 m/s. The speed of sound in steel is approximately 5900 m/s. If your friend strikes one end of a steel pipe with a hammer while you listen at the other end, you will hear two distinct sounds: one traveling through the air and the other traveling through the steel pipe. If the pipe is 1.94 seconds elapses between the two distinct sound, how long is the steel pipe.
Assume the speed of sound in air is 340 \text{ m/s}340 m/s340, start text, space, m, slash, s, end text. The frequency of the musical note Middle C is 261.63 \text{ Hz}261.63 Hz
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To calculate the length of the steel pipe, we can use the formula:
Distance = Speed * Time
We know that the speed of sound in air is approximately 340 m/s and the speed of sound in steel is approximately 5900 m/s.
Let's assume that the sound travels through the steel pipe first and then through the air.
Let's denote the length of the steel pipe as "L".
The time it takes for the sound to travel through the steel pipe would be:
Time_steele = L / 5900
The time it takes for the sound to travel through the air would be:
Time_air = L / 340
Given that there is a time lapse of 1.94 seconds between the two distinct sounds, we can set up the equation:
Time_steele + Time_air = 1.94
Substituting the values for the respective times:
L / 5900 + L / 340 = 1.94
Multiplying through by the least common multiple of the denominators (5900 * 340) to clear the fractions:
340L + 5900L = 1.94 * 340 * 5900
Simplifying:
6240L = 3887960
Dividing by 6240 on both sides to solve for L:
L = 3887960 / 6240
L ≈ 622.76 meters
Therefore, the length of the steel pipe is approximately 622.76 meters.
To find the length of the steel pipe, we can use the equation:
Distance = Speed × Time
First, we need to find the distance traveled by the sound through the air. The speed of sound in air is approximately 340 m/s, and the time between the two sounds is 1.94 seconds. Therefore, the distance traveled by the sound through the air is:
Distance_air = Speed_air × Time
= 340 m/s × 1.94 s
= 659.6 m
Next, we need to find the distance traveled by the sound through the steel pipe. The speed of sound in steel is approximately 5900 m/s. Since the sound traveled through both air and steel, the total distance traveled by the sound is equal to the sum of the distances through air and steel. Therefore, we can write:
Distance_total = Distance_air + Distance_steel
Since we know the total distance traveled (equal to the length of the steel pipe) and the distance traveled through air, we can solve for the distance traveled through steel:
Distance_steel = Distance_total - Distance_air
= Length_steel_pipe - 659.6 m
Now, we can substitute the given time and speeds to solve for the length of the steel pipe:
Length_steel_pipe - 659.6 m = Speed_steel × Time
Length_steel_pipe = Speed_steel × Time + 659.6 m
= 5900 m/s × 1.94 s + 659.6 m
= 11426 m + 659.6 m
= 12085.6 m
Therefore, the length of the steel pipe is approximately 12085.6 meters.