A steel bar, the narrower of the two seen in the photograph below, is struck near its center with a rubber mallet to produce a musical tone as shown in an mpeg video when you click your mouse on the photograph.

 

 

A second steel bar, with the same length and thickness, but twice the width, as seen in the photograph, also produces a tone when struck. The question this week is about the frequency relation between the two tones.

When the two steel bars are struck, relative to the frequency of the narrower bar, the frequency of the wider bar will be:

• (a) higher.
• (b) lower.
• (c) the same.

 

After April 3, click Read More for the answer.

The answer is (c): the frequency of the wider bar will be exactly the same as that of the narrower bar, as can be heard on this mpeg video.

 

The transverse standing waves excited in these two bars by striking them as seen in the video are the same. Each has an antinode in the center, nodes approximately at the points where they rest on the rubber supports, and antinodes approximately at the ends (although not quite, because of the rigidity of the bars). The fact the width of the two bars is different has little bearing on the rate at which they vibrate in this transverse mode. The relevant physical quantities are the mass per unit length of the bar relative to its ability to bend, which is the same for both bars; both quantities increase in the same manner as the bar becomes wider.