An ultrasonic tape measure uses frequencies above 20 MHz todetermine dimensions

Question

An ultrasonic tape measure uses frequencies above 20 MHz todetermine dimensions of structures such as buildings. It does so byemitting a pulse of ultrasound into air and then measuring the timeinterval for an echo to return from a reflecting surface whosedistance away is to be measured. The distance is displayed as adigital read-out. A tape measure emits a pulse of ultrasound with afrequency of 25.0 MHz. (a) What is the distance to an object fromwhich the echo pulse returns after 24ms when the air temperature is 26°C?
1 m
(b) What should be the duration of the emitted pulse if it is toinclude 10 cycles of the ultrasonic wave?
2 µs
(c) What is the spatial length of such a pulse?
3 mm (a) What is the distance to an object fromwhich the echo pulse returns after 24ms when the air temperature is 26°C?
1 m
(b) What should be the duration of the emitted pulse if it is toinclude 10 cycles of the ultrasonic wave?
2 µs
(c) What is the spatial length of such a pulse?
3 mm

Explanation / Answer

frequency of pulse f = 25.0 Mhz (a)echo pulse returns t = 24 ms air temperature T = 26°C required distance be d We know f' = f * (v + vo/v - vs) f' = (1/2t),v = 340 m/s,vo= 0,vs=(d/(t/2)) = (2d/t) substituting we get d = (v/2) * t2 * (1/t - f) (b)duration of emitted pulse t = (1/10f') = (1/20t) ---------------(2) (c)spatial length of pulse = v * t (from equation (2))

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