Longitudinal Standing Waves in a Solid. ?Longitudinal standing waves can be produced in a solid rod by holding it at some point between the fingers of one hand and stroking it with the other hand. The rod oscillates with antinodes at both ends. (a) Why are the ends antinodes and not nodes? (b) The fundamental frequency can be obtained by stroking the rod while it is held at its center. Explain why this is the ?only ?place to hold the rod to obtain the fundamental. (c) Calculate the fundamental frequency of a steel rod of length 1.50 m (see Table 16.1). (d) What is the next possible standing-wave frequency of this rod? Where should the rod be held to excite a standing wave of this frequency?
Solution 66P Step 1 The steel ro d has standing waves much like a pipe open at both ends, since the ends are both displacement antinodes. An integral number of half wavelengths must fit on the rod, nv That is,fn= 2L Where n is an integer Given v=5941 m/s L=1.50 m