Frequency of waves

FelicitaH

There are two parts to this question. I got the first part and thought the second would be relatively easy to answer, but I keep getting it wrong:

Ocean waves are traveling to the east at 3.2 m/s with a distance of 22m between crests.

a) With what frequency do the waves hit the front of the boat when the boat is at anchor? ** 3.2/22=.1455 Hz, which I got right.

b) With what frequency do the waves hit the front of a boat when the boat is moving westward at 1.4m/s?

Now, b/c they are moving towards each other, I substrated 1.4 from 3.2 and I got 1.8. I then got 1.8/22=0.0818, which is incorrect.

What am I doing wrong with regard to the second part?

Saketh

If you are walking towards a wave, will the wave hit you more frequently or less frequently? Will it seem like the wave is moving faster or slower?

Similarly, will a boat moving towards the wave be hit with a higher or lower frequency than it would were it at rest?

Ask yourself these questions, and you will see if you did something incorrectly.

FelicitaH

Ok. It would be hit at a greater frequency, so I should add instead of substracting?

That confuses me... because I thought that if two waves were moving toward each other it was destructive (or something like that) and so you would subtract from one another. At least, that's how I understood what my prof was saying.

Saketh

But is the boat a wave?

When two waves collide, they can cancel each other out if their characteristics meet certain requirements. You understood your professor correctly.

(Disclaimer: It turns out that the boat (and all matter) has a wave component given by one of de Broglie's equations. But you don't need to worry about that, as it is a negligible component.)

FelicitaH

I just assumed I could consider the boat a wave. Not sure why.

So -- 1.4 + 3.2 = 4.6/22 = .2091

Is that correct then? I only have one more chance to answer this question correctly, which I why I'd just like to make sure, if that's possible.

*EDIT* Actually, that's wrong. That was an answer that I tried earlier...

Saketh

The logic is sound, and the math appears correct. The question is - do you think it is the right answer?

FelicitaH

Yeah, it's not right. I tried that answer earlier. Apparently it's too small.

sdekivit

my approach is nothing different than what has been done before, but assume the boat is at a point B 22 m eastwards of point A where the first wave is approaching.

When the wave collides the boat they both have travelled a distance total of 22 m, thus:

[tex]3.2\cdot t + 1.4 \cdot t = 4.6\cdot t = 22 \Rightarrow t = 4.8 s[/tex]

Then the next wave is again at a distance 22 m and collides after 4.8 seconds.

--> thus the frequency = 1/4.8 = 0.208 Hz