84. Let be the length of the rod. Then the time of travel for sound in air (speed vs ) will be ts = /vs . And the time of travel for compressional waves in the rod (speed vr ) will be tr = /vr . In these terms, the problem tells us that 1 1 − ts − tr = 0.12 s = . vs vr Thus, with vs = 343 m/s and vr = 15vs = 5145 m/s, we ﬁnd = 44 m.