Interpreting questions like this (About waves)

[superconduct]

Homework Statement

Given that high tide occurs twice each day. What is the tidal frequency in Hz?

Homework Equations

frequency in Hertz = no. of complete cycles per second

The Attempt at a Solution

Since the there is only one wave cycle between 2 high tides
Frequency=1/(24x3600)

4. My inquiries
The model answer in my workbook is frequency=2/(24x3600). It is very unclear just from the question whether 1 wave or 2 waves are completed. But since it only said "high tide occurs twice each day" and it didn't say if there are 2 low tides or 1 low tide, I personally think it would be reasonable to think only 1 wave cycle occurred in one day.

Another question in my workbook that I have similar inquiry with is this: The diagram( a slinky with 5 compressions and 4 rarefactions in between, if anyone wants the diagram I can upload it though I doubt it would be necessary) shows a longitudinal wave traveling along a slinky of length 12cm. If five compressions are produced in each second, calculate the speed of the wave.
Since my main trouble with this is the interpretation of the wordings for deducing the frequency, this question can be simplified to: If 5 compressions are produced in each second, what is the frequency of the wave?

In alignment to my thinking process for the 1st question, here my way to tackle it would be
Frequency= 4/1= 4Hz because there are exactly 4 complete wave cycles produced in each second
But sadly, the model answer is frequency=5/1=5Hz.

I don't know if my interpretation or concepts have any flaws or errors. Please let me know if I have. This is very important as misinterpretation of wordings in an exam can lead to a heavy deduction of marks, which does not reflect the real ability of the student in physics but in word interpretation in the examiner's way.

So, is my answer or the model answer correct?

 

[Orodruin]

But since it only said "high tide occurs twice each day" and it didn't say if there are 2 low tides or 1 low tide, I personally think it would be reasonable to think only 1 wave cycle occurred in one day.

How can there be only 1 low tide if there are 2 high tides?

The point is that the tidal forces make the high tide rise on opposite sides of the Earth (and equivalently, low tides also appear on opposite sides of the Earth).

 

[superconduct]

How can there be only 1 low tide if there are 2 high tides?

The point is that the tidal forces make the high tide rise on opposite sides of the Earth (and equivalently, low tides also appear on opposite sides of the Earth).

The question is considering the number of tides at one side, it means 2 high tides occurred one after another at one side. So at that side there could be 1 low tide or 2 low tides if the question only says 2 high tides occurred i.e. 2 possibilities, right?

Also, what are your thoughts about the slinky problem?

 

[Orodruin]

The question is considering the number of tides at one side, it means 2 high tides occurred one after another at one side. So at that side there could be 1 low tide or 2 low tides if the question only says 2 high tides occurred i.e. 2 possibilities, right?

Not right. You have to realize that the position of the tides relates to how the Earth rotates in relation to the tidal waves. During 24 hours, the Earth rotates one time around its axis and therefore a given position on the surface will pass through each of the tidal waves, giving 2 tidal wave highs and 2 tidal wave lows per 24 hours. It is very unclear what you mean with "one after another at one side". You cannot have two local maxima without a local minimum in between.

 

[Orodruin]

I think I see your problem. You think that "occurring twice per day" means that if you start the clock at the first high, then the second high will be the high coming up 24 hours later. This is not the case. It means that, regardless of when you start your clock, 24 hours later you will have observed two highs. If you happen to start your clock exactly on the high, you should only count it as half a high.

 

[superconduct]

I think I see your problem. You think that "occurring twice per day" means that if you start the clock at the first high, then the second high will be the high coming up 24 hours later. This is not the case. It means that, regardless of when you start your clock, 24 hours later you will have observed two highs. If you happen to start your clock exactly on the high, you should only count it as half a high.

If we consider a high tide as a maximum point, then "2 high tides a day" should mean 2 maxima with 1 minimum and thus 1 wave cycle in total?

Let's say: a string produces 2 maxima per second, then do you consider its frequency as 1 Hz or 2 Hz?

 

[Orodruin]

If we consider a high tide as a maximum point, then "2 high tides a day" should mean 2 maxima with 1 minimum and thus 1 wave cycle in total?

No. There is no other way of saying this other than that you are making an interpretation the rest of the world does not agree with. If you want to maintain 2 highs per day, you also need two lows.

Let us put it this way, if you extend the period you are looking at to two days, how many highs do you have? What if you extend it to 1000 days? The number of highs per day is the limit when the number of days goes to infinity.

Yet another way of seeing it is that you must decide which day a high corresponds to, you are not allowed to count it for two different days.

 

[superconduct]

No. There is no other way of saying this other than that you are making an interpretation the rest of the world does not agree with. If you want to maintain 2 highs per day, you also need two lows.

Let us put it this way, if you extend the period you are looking at to two days, how many highs do you have? What if you extend it to 1000 days? The number of highs per day is the limit when the number of days goes to infinity.

Yet another way of seeing it is that you must decide which day a high corresponds to, you are not allowed to count it for two different days.

If I extend it to 2 days, then there would be 3 maxima and 2 minima in my understanding. So for n days there would be (n+1) highs provided that a high means a maximum but not a section of wave with positive displacement.

Could you answer my question(Answering this will help me understand better): A string produces 2 maxima per second, then do you consider its frequency as 1 Hz or 2 Hz?

 

[Orodruin]

I have already answered it, the correct answer is 2 Hz. You cannot count the same maxima as belonging to two different seconds.

 

[superconduct]

You cannot count the same maxima as belonging to two different seconds.

Why?

 

[Orodruin]

Why?

Because then you are double counting them and it is not "per second" they become shared between two seconds. The "per second" means the number of full periods you can fit into one second.

 

[superconduct]

Because then you are double counting them and it is not "per second" they become shared between two seconds. The "per second" means the number of full periods you can fit into one second.

Thank you for explaining to me and your patience :D
I understand now after combining the two premises: It cannot be recounted in another second; Extending would yield recounting.