A technician uses ultrasound to identify a stone sample. The sample is known to be sandstone, limestone or granite.
The sample is 0.045 m thick. A probe sends a pulse through the sample. The pulse reflects from the opposite face and returns to the probe after 20 μs20\ \mu\text{s}20 μs.
The wave speed can be calculated using
v=2dtv=\dfrac{2d}{t}v=t2d
where
d d\,d is the thickness of the sample
t t\,t is the time taken for the echo to return.
The table gives measurements obtained from reference samples.
| Stone | Speed of ultrasound in m/s\text{m/s}m/s |
|---|---|
| sandstone | 3000 |
| limestone | 4500 |
| granite | 6000 |
The technician can use either of two probes to examine boundaries between thin layers in another stone sample.
| Probe | Wavelength in the stone in mm\text{mm}mm |
|---|---|
| R | 3.0 |
| S | 0.75 |
Give the echo time in seconds.
Calculate the speed of the ultrasound in the sample and use the reference measurements to identify the stone.
State which probe, R or S, should be used to distinguish boundaries that are close together.
Give a reason for your answer.