Fig. 1 shows an engineer checking a steel railway axle for an internal crack. A probe sends a short ultrasound pulse into one end of the axle. Echo A is ref...
Question 1 Report
Fig. 1 shows an engineer checking a steel railway axle for an internal crack. A probe sends a short ultrasound pulse into one end of the axle. Echo A is reflected from a crack and echo B is reflected from the far end. On the display, echo A returns before echo B. The velocity of ultrasound in the steel is 6000 m/s. The engineer uses the time between sending the pulse and receiving echo A to calculate the crack position. This non-destructive test allows the axle to remain in use if no dangerous flaw is found.
(a) What causes echo A? [1]
(b) Explain why echo A returns before echo B. [1]
(c) The time for echo A is 0.00020 s. Calculate the distance of the crack from the probe. [2]
(d) Give one advantage of this test over cutting the axle open. [1]
An organ builder tests two open pipes, shown in Fig. 1, using the same air supply. Pipe P is 0.50 m long and pipe Q is 1.00 m long. Both pipes are open at their top and bottom ends. The builder hears a note from each pipe and wants to choose the pipe that produces the lower note for a church organ. Air particles inside each pipe vibrate and form a standing wave. The sound then travels through the air to the listener. The figure shows only the length of each pipe, not the wavelength of the sound waves.
(a) Which pipe produces the lower-pitched note? [1]
(b) Explain your answer using the wavelength in each pipe. [2]
(c) Describe how the particles of air move as sound travels along a pipe. [2]
Answer Details
Ultrasound testing of an axle
(a) Echo A is caused by reflection of ultrasound from the crack. [1]
(b) Echo A returns before echo B because the crack is closer to the probe than the far end of the axle. [1]
(c) The measured time is for the pulse to travel to the crack and then return, so first calculate the total path length:
\[\text{total distance}=6000\ \text{m s}^{-1}\times0.00020\ \text{s}=1.2\ \text{m}\]
[1]
The crack distance is half this round-trip distance:
\[\text{distance from probe}=\frac{1.2}{2}=0.60\ \text{m}\]
[1]
(d) The test does not damage the axle. [1] It may also be credited because it is quicker or can locate an internal flaw.
Open organ pipes
(a) Pipe Q produces the lower-pitched note. [1]
(b) Pipe Q supports a longer wavelength than pipe P. [1] For sound in the same medium, wave speed is the same and \(v=f\lambda\). A longer \(\lambda\) therefore means a lower \(f\), so the pitch is lower. [1]
(c) Air particles vibrate back and forth parallel to the direction in which the sound travels. [1] The particles do not move all the way along the pipe with the wave; they oscillate about fixed positions. [1]
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