Waves and Energy Transfer?

Question

1. Two boats are anchored 4 m apart. They bob up and down every 3 s, but when one is up, the other is down. There are never any wave crests between the boats. Calculate the velocity of the waves.

2. A standing wave in a clothesline has 4 nodes and 3 antinodes. The clothesline is 12 m long and is vibrating at 0.50 vibrations per second. What is the speed of the wave?

3. A sound wave travels from A to B in the diagram below.
A ------------------------> B
In which directions do the particles of the medium vibrate?
a. up/down
b. left/right

My teacher did not teach us ANY of these concepts, except the ultilization of v=(wavelength)(frequency). I do not know what a node or antinode is, and the other two problems confuse me. Thank you for your help!

Answer 1

1. Since they are 4 m apart and one is down as the other one is up we know that one of in the valley of the wave while the other one in riding the crest. Thus

T= period= 2 (3)=6 sec
then f=1/T=1/6 Hz
L= wavelength=2(4)=8m
then velocity
v=L f= L/T=8/6=4/3 m/sec

2. Draw a picture as it will aid understanding
The wavelength is can be measured between points where a wave begins to repeat itself like between two nearest peaks or two nearest valleys.
l=(12/3)2= 8m
v= l f
But what is frequency!(see reference)
We know that the input frequency is .5 Hz but we have a 3/2 of a wave so;
f = 3/2f(fundamental)=(3/2)0.5=3/4 Hz
v= 8 (3/4)=6m/s

3. As the wave propagates left to right the particles of air will move from left to right and back from right to left. That may sound a bit confusing however if you think of it as a pressure wave(which it is) it makes sense.