4.164. Fee Fig. 35, for (a) and (b); see Fig. 36 for (c).
4.165. (a) ivp = 1/2pa2w2 sin2 kx•cos2 wt; (b) wk = 1 /2pa2w2 X
X cost kx• sin2 wt. See Fig. 37.
0(/27,z.
t=T/2
4(r)
Fig. 35.
4.166. amus = 5 mm; to the third overtone.
4.167.— 1712 (1 +111) = 1.4.
vi
r 711 (1+112)
4.168. Will increase
2 times.
11= 17 1 1-1- 1-f/IT
at
Fig. 36.
Fig. 37.
4.169. v = 21v = 0.34 km/s.
4.170. (a) vn = ir (2n +1), six oscillations; (b)
also six oscillations. Here n=0, 1, 2, ...
2n-1-1 VT
4.171. v7,—
— -- 3.8 (2n+1) kHz; four oscillations with
2/
p
frequencies 26.6, 34.2, 41.8, and 49.4 kHz.
4.172. (a) Tmax- ---- 1/47nw24nax; (b) (T)= 1/8m(024nax•
4.173. W = 1 /jcSpw2a2/k.
4.174. v = 2v ovu/ (v2 — u2)
2vou/v = 1.0 Hz.