Interference of ultrasonic waves by a Lloyd mirror 1.5.20-00

Interference of ultrasonic waves by a Lloyd mirror 1.5.20-00 Principle:

What you can learn about … Longitudinal waves Superposition of waves Reflection of longitudinal waves Interference

2 Slide mount f. opt. profile-bench 08286.00

1 What you need: Complete Equipment Set, Manual on CD-ROM included Interference of ultrasonic waves by a Lloyd mirror P2152000

1 Connecting cord, l = 50 cm, blue 07361.04

1 Connecting cord, l = 50 cm, red 07361.01

1 Measuring tape, 2 m 09936.00

1 Screen metal, 30⫻30 cm 08062.00

1 Swinging arm 08256.00

1 Sliding device, horizontal 08713.00

A partial packet of radiation passes directly from a fixed ultrasonic transmitter to a fixed ultrasonic receiver. A further partial packet hits against a metal screen that is positioned parallel to the connecting line between the transmitter and receiver, and is reflected in the direction of the receiver. The two packets of radiation interfere with each other at the receiver. When the reflector is moved parallel to itself, the difference in the path lengths of the two packets changes. According to this difference, either constructive or destructive interference occurs.

The received signal as a function of the reflector distance d.

1 Base f. opt. profile-bench, adjust. 08284.00

1 Optical profile-bench, l = 60 cm 08283.00

1 Digital multimeter 07134.00

1 Ultrasonic receiver on stem 13902.00

1 Ultrasonic transmitter on stem 13901.00

1 Power supply f. ultrasonic unit, 5 VDC, 12 W 13900.99

Ultrasonic unit 13900.00

Tasks:

2. The d values of the various maxima and minima are to be determined from the U = U(d) graph and compared with the theoretically expected values.

1. The sliding device is to be used to move the reflector screen positioned parallel to the connecting line between the transmitter and receiver parallel to itself in steps of d = (0.5-1) mm. The reflector voltage U is to be recorded at each step.

2 Slide mount f. opt. profile-bench, h = 80 mm 08286.02

1.5.20 -00

Interference of ultrasonic waves by a Lloyd mirror

1 Connecting cord, l = 50 cm, red 07361.01

Longitudinal waves, superposition of waves, reflection of longitudinal waves, interference.

Principle

A partial packet of radiation passes directly from a fixed ultrasonic transmitter to a fixed ultrasonic receiver. A further partial packet hits against a metal screen that is positioned parallel to the connecting line between the transmitter and receiver, and is reflected in the direction of the receiver. The two packets of radiation interfere with each other at the receiver. When the reflector is moved parallel to itself, the difference in the path lengths of the two packets changes. According to this difference, either constructive or destructive interference occurs.

Equipment

Ultrasonic unit 13900.00

1 Power supply f. ultrasonic unit, 5 VDC, 12 W 13900.99

Set up the experiment as shown in Fig. 1, referring to the diagram in Fig. 2 for more clarity.

Set-up and procedure

2. The d values of the various maxima and minima are to be determined from the U = U(d) graph and compared with the theoretically expected values

1. The sliding device is to be used to move the reflector screen positioned parallel to the connecting line between the transmitter and receiver parallel to itself in steps of d = (0.5-1) mm. The reflector voltage U is to be recorded at each step.

1 Tasks

1 Connecting cord, l = 50 cm, blue 07361.04

Related topics

Mount the ultrasonic transmitter and the ultrasonic receiver in their slide mounts (h = 80 mm). Set them at the same height

1 Swinging arm 08256.00

1 Screen metal, 30x30 cm 08062.00

1 Measuring tape, 2 m 09936.00

1 Sliding device, horizontal 08713.00

2 Slide mount f. opt. profile-bench, h = 80 mm 08286.02

1 Base f. opt. profile-bench, adjust. 08284.00

1 Optical profile-bench, l = 60 cm 08283.00

1 Digital multimeter 07134.00

1 Ultrasonic receiver on stem 13902.00

1 Ultrasonic transmitter on stem 13901.00

then orient them on the optical bench so that their middle axes are concordant and in alignment with the optical bench. Use the swinging arm to mount the reflector screen on the sliding device (horizontal) and ensure that the slide of this is initially situated at the start of the scale At the start of the experiment the reflector screen must be aligned parallel to the optical bench and at a distance of 2 cm from the middle axis of the transmitter and receiver. Carry out this adjustment by turning the swinging arm, keeping the reflector parallel to the optical bench while doing so.

Fig.1: Experimental set-up

2 Slide mount f. opt. profile-bench 08286.00

Interference of ultrasonic waves by a Lloyd mirror

1.5.20 -00

fier in the saturation range. Should such a case occur and the “OVL“ diode light up, reduce either the transmitter amplitude or the input amplification. To start with, for control and avoid- ance of overloading, use the sliding device to bring the screen to the area of the 1st maximum of the measurement curve.

To now record the measurement curve, use the sliding device to move the screen away from the middle axis of the system in steps of d = (0.5 – 1) mm, measuring the appropriate

∆

receiver voltage U at each step. The results of such a measurement series are shown in Fig. 3.

Theory and evaluation

Fig. 4 shows the paths of the partial packets from the sound wave emitted by the transmitter which interfere with each other at the receiver. Part of the wave reaches the receiver directly, whereas a second part is first reflected by a metal screen. According to the difference in the path lengths of the

Fig. 2: Diagram of the experimental set-up two packets either constructive or destructive interference (t = transmitter, r = receiver, sd = sliding device, sa = occurs. With a constant distance between transmitter and swinging arm, sc = screen) receiver, the difference in the paths lengths (and with this the

∆

interference conditions) is a function of the distance d of the reflector from the middle axis (see Fig. 4). Finally move the transmitter and receiver so that their front edges are symmetrical to the sides of the screen and at a dis-

The following is valid: tance of 29.4 cm apart (see Fig. 2). As the active parts of the ultrasonic elements are approx. 3 cm behind their protective grids, their effective distance apart is now 30 cm.

(1) ¢ ⫽ 2 1y ⫺ x2 ⫽ 2 a 21d ⫹ x 2 ⫺ x b

Connect the transmitter to the TR1 diode socket of the ultrasonic unit and operate it in continuous mode “Con“. Connect Constructive interferences (maxima) are given, when corre-

∆ the receiver to the left BNC socket (prior to the amplifier).

sponds to a whole-numbered wavelength of the ultrasonic Connect the signal received to the analog output of the digital wave: multimeter to have it displayed subsequent to amplification and rectification. To ensure proportionality between the input

¢ ⫽ nl ⫽ 2 a 21d ⫹ x 2 ⫺ x b signal and the analog output signal, avoid operating the ampli- (2)

l n ⫹ nlx ; n ⫽ 0, 1, 2, 3, ... S d ⫽ B

4 Destructive interferences (minima) are given, when corre-

∆

sponds to an odd-numbered half-wavelength of the ultrasonic wave: 2n ⫹ 1

¢ ⫽ l ⫽ 2 a 21d ⫹ x 2 ⫺ x b

2 (3)

2n ⫹ 1 2n ⫹ 1

l b ⫹ lx ; n ⫽ 0, 1, 2, 3, ... S d ⫽ B a

2 Fig.4: Diagram for the calculation of the path length difference of the two partial packets Fig.3: The signal received U as a function of the reflector dis-

(t = transmitter, r = receiver, sc = screen) tance d.

Interference of ultrasonic waves by a Lloyd mirror

1.5.20 -00

Table 1 lists the d values for the maxima and minima in Fig. 4, The following values were used to calculate d: x = 15.0 cm and l = 0.86 cm. and also, for comparison purposes, the d values calculated using equations (2) and (3)..

As the transmitter emits at a frequency of f = 40 Hz, it follows

from c = l · f (c = 343.4 ms at T = 20°C) that the ultrasound Table 1: d values at the maxima and minima wavelength is: l = 0.858 cm 0.86 cm.

⬵ As only the d values of the extremes are determined in this

Maxima Minima experiment and not their absolute intensity, factors such as absorption by air and the type of wave (plane or spherical)

/cm /cm /cm /cm n d d d d

exp. theor. exp. theor.

need not be considered here.

2.50

2.55

3.55

3.62

4.35

4.44

5.00

5.15

5.60

5.78

6.15

6.35

6.65

6.88

7.15

7.38

1.5.20 -00

Interference of ultrasonic waves by a Lloyd mirror

Interference of ultrasonic waves by a Lloyd mirror 1.5.20-00