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°C?
m
(b) What should be the duration of the emitted pulse if it is to include 10 cycles of the ultrasonic wave?
µs
(c) What is the spatial length of such a pulse?
mm

Answer 1

To find the solution of this question we have to find the speed of sound at temperature which is given by equation :

speed of sound ,

V = 331 +0.606T m/s = 331 +0.606 x 26 = 347m/s

(A) Here total distance travelled by the sound to return back ,

2d=V x Time

  

d= 347m/s x 25ms -= 4.33m

(B) Duration of the emitted  pulse for 10 cycles , (f= frequency =24MHz)

,

T = 10 x1__10 = 4.17 x 10-'s = 0.417us

(C) spatial length

   ,

X=uXT = 347 x 0.417 = 144.7 x 10-6m = 0.1447mm