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Wave speed in a solid

In this activity you can measure the speed of a longitudinal wave in a metal rod. As one end of the rod is hit with a hammer, so the hammer remains in contact until the pulse returns from the far end of the rod.

Introduction

This Science experiment is adapted from the Salters Horners Advanced Physics Project. It corresponds to Activity 18 from the ‘Build or Bust’ section of the course.

The time of contact of the hammer and rod, and their breaking contact, is found by reference to how the voltage changes to the input of Pico DrDAQ educational data logger, or ADC-42. Such a change is shown in Figure A18.1, the start of the rise in the trace indicating the time of contact of the hammer and rod, and the start of the fall indicating where the hammer lost contact with the rod. The time between is (i) the length of time that the hammer was in contact with the rod and (ii) the time it took for the longitudinal wave pulse to travel to the far end of the rod and back.

Wave Speed in a Solid - Typical trace

Figure A18.1: typical trace

Procedure

Clean the hammer head and the end of the rod that is to be hit with emery cloth. If necessary, also clean the places where electrical contact is to be made on the hammer and the bar by connecting leads. This will ensure good electrical contact in the circuit.

Suspend the metal rod on two fairly long elastic bands from clamps on two retort stands. Connect up the circuit shown in Figure A18.2 to include the metal rod, hammer, 3 V battery and leads to Pico DrDAQ or ADC40/42. Load PicoScope.

Wave speed in a solid - Circuit connections.

Figure A18.2: circuit connections.

With the DrDAQ, select the oscilloscope display if it is not already on the screen. Select Volts, Y gain x 1 for Input A. Leave the other inputs off. Set the Timebase at 1 ms/div; the X gain to x 2; the Trigger to Single, Rising and 70 mV*; and the Display setting (right-hand box at the foot of the screen) to -10%. You can adjust both the X and Y gains afterwards if the trace does not display as you would wish. Click GO and hit the end of the metal rod with the hammer.

With the ADC-40/42 select the oscilloscope display if it is not already on the screen. Set the Timebase at 1 ms/div; the X gain to x 2; the Y gain to x 1; the Trigger to Single, Rising and 70 mV*; and the Display setting (right-hand box at the foot of the screen) to -10%. You can adjust both the X and Y gains afterwards if the trace does not display as you would wish. Click GO and hit the end of the metal rod with the hammer.

*You may be able to reduce this value but it must be high enough to prevent triggering too early.

Measure the length of the metal rod.

Analysis of results

Click the cursor on the point where the trace just begins to rise and note the time trise at which this occurred. Now click the cursor on the point where the trace just starts to fall and note the time tfall at which this occurred. The difference in these times is the time of contact of the hammer with the metal rod.

Calculate and note the speed of the longitudinal wave pulse down the metal rod.

The speed vlongitudinal of a wave pulse in a solid is given by the expression:

  where E is the material’s Young Modulus and its density. For aluminium E = 7.0 x 1010 Nm-2 and = 2.7 x 103 kg m-3. For steel E = 2.0 x 1011 Nm-2 and = 7.8 x 103 kg m-3.

Compare your experimental values with those obtained with the above expression.

NOTE: You will probably find some difference between the values obtained as much depends on the extent to which (i) the metal is anisotropic - not having the same properties in all directions, (ii) the degree of cold working it underwent during manufacture, (iii) E and  vary with temperature (iv) shearing forces also come into play so that the speed depends not just on the Young Modulus but also on the Bulk Modulus and (v) the uncertainty of your experimental results.

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