An ultrasonic tape measure uses frequencies above 20 mhz to...

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 the 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

Transcript

00:01 Hi there, so for this problem we are called that ultrasonic tape measure uses frequencies that are about 20 megahertz.

00:14 So to determine dimensions of structures such as buildings, it does so by emitting a pulse of ultrasonic into earth and then measuring the time interval for an echo to return from a reflecting surface whose distance away is to be measured.

00:36 Now the distance is displayed as a digital red -out, a tape measure emits a pulse of ultrasound with a frequency that is given that is 24 megahertz.

00:59 So with that said for part a of this problem, we are asked about what is the distance to an option from which which the echo pulse returns after 24 milliseconds.

01:16 So the interval of time is 24 milliseconds, that is 24 times 10 to the minus 3 seconds.

01:25 When the earth, it is at a temperature of 26 celsius degrees.

01:33 So first we need to calculate the sound speed, because we know that the sound speed depends on the temperature.

01:44 So that equation is the speed that we know, 331 meters per second, and this plus a constant that is 0 .6 meters per second per celsius degrees, and this times the temperature, in this case, 26 celsius degrees.

02:08 Degrees.

02:09 So from this we obtain a value of 347 meters per second.

02:20 So that's the solution for part a of this problem.

02:27 Now for part b, we are asked about what should be the duration of the emitted pulse if it is to include 10 cycles of the ultrasonic wave? so in this part of the problem, if we let that delta t is the direction of the poles, we know that that should be equal to 10 times the wavelength divided by the speed.

03:15 So we know also that the velocity is just the part between the frequency and the wave...

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