An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions

Question

An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions of structures such as buildings. It does so by emitting a pulse of ultrasound into air and then measuring the time interval for an echo to return from a reflecting surface whose distance away is to be measured. The distance is displayed as a digital read-out. A tape measure emits a pulse of ultrasound with a frequency of 24.0 MHz.

(a) What is the distance to an object from which the echo pulse returns after 24 ms when the air temperature is 26

Explanation / Answer

First, find the speed of sound at 26C

v = 331.3 + .606 * T
T is in deg C
v = 331.3 + .606 * 26
v = 347 m/s

Ref: http://en.wikipedia.org/wiki/Speed_of_so...

a. Find Distance:
2d = v*t
d = 1/2 (347 m/s) ( 24 ms)
d = 4.16m

b. duration of pulse

t = 10 * 1/f
t = 10/ 24x10^6 Hz
t = 4.167 x10^-7 sec

c. spatial length of pulse
d = v * t
d = 347 m/s * 4.167x10^-7 sec
d = 1.446 x 10^-4 m

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