Question

the speed of ultrasound in a faulty metal there is 5,000m/s . ow far away is a crack in the metal if the ultrasound wave was sent through the metal and it reflected back from the crack to the detector in 0.01 m/s?

Answer 1

To find the distance to a crack detected by reflected ultrasound, multiply the speed of ultrasound by half the total reflection time. With a speed of 5,000 m/s and a reflection time of 0.01 s, the calculation shows that the crack is 12.5 meters away from the detector.

Step-by-step explanation:

To determine how far away a crack in the metal is based on the ultrasound reflection time, we use the formula d = v \( t / 2 \), where d is the distance to the crack, v is the speed of sound in the metal, and t is the total travel time of the ultrasound wave (to the crack and back). In this case, the speed of ultrasound in the metal is given as 5,000 m/s, and the reflection time is 0.01 seconds.

Let's perform the calculation step by step:

• Calculate the total distance traveled by the ultrasound wave by multiplying the speed (v = 5,000 m/s) by the total time it took for the wave to travel to the crack and back (t = 0.01 s): Total distance = v \( t / 2 \).
• Since the wave has to travel to the crack and return back to the detector, we divide the total travel time by 2 to find the time it took for the sound to reach the crack. Therefore, Total distance = 5,000 m/s \( 0.01 s / 2 \).
• This yields a total distance traveled of 25 meters. However, this is the round trip distance, so the crack is half of this distance away from the detector, meaning the crack is located 12.5 meters away.

Therefore, the crack in the metal is 12.5 meters away from the ultrasound source or detector.