Question

A periodic transverse wave is established on a string such that there are exactly two cycles traveling along a 3.0-m section of the string. The crests move at 20.0 m/s.

14. What is the frequency of the wave?
(a) 0.67 Hz (c) 13 Hz (e) 57 Hz
(b) 1.33 Hz (d) 30 Hz

15. What is the shortest horizontal distance from a crest to a point of zero acceleration?
(a) 0.38 m (c) 1.5 m (e) 6.0 m
(b) 0.75 m (d) 3.0 m

16. How long does it take a particle at the top of a crest to reach the bottom of an adjacent trough?
(a) 0.018 s (c) 0.075 s (e) 0.30 s
(b) 0.038 s (d) 0.150 s

Answer 1

2 cycles on a 3.0m string indicates \[2\lambda=3.0\], so\[\lambda=1.5m\] and we have crests travelling at 20m/s ,which implies velocity of the wave is 20m/s.
V=20m/s. & we know,\\[V=\lambda/T\], where T is the time period, so calculating for "T" we get [T=13.33Hz]

Answer 2

and for the shortest horizontal distance,

the point A shown is the point with zero acceleration. so horizontal distance of a from the adjacent crest is\[\lambda/4\]so , the answer to the 2nd question is 1.5/4=0.38
option a)0.38 is your answer.