Optimizing Boat Frequency: Eastward vs. Westward 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]

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.

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 traveled a distance total of 22 m, thus:

$$3.2\cdot t + 1.4 \cdot t = 4.6\cdot t = 22 \Rightarrow t = 4.8 s$$

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