Calculate Wavelength from two sinusoidal waves

[Elizabeth]

This is my first posting ever ! I hope someone can point me in the right direction. Please also note, that I'm on a Music Technology course, but there are quite a lot of physics/maths!

Presenting Problem
The air pressure is found to be normal atmospheric pressure 2 metres from a sinusoidal sound source. At the same instant, at 2.5 metres distantance from the source, the air pressure has risen to a maximum value above normal atmopsheric pressure.
Assuming the air pressure between two points is only rising, what is the wavelength of the sound?

Formauls/Relevant Equations.
There are no formalus offered.


My Attempt
I've been able to ascertain that the wavelength is the distance pressure waves travel in the time it takes the source to complete one cycle.
I've tried to think of a sinusoidal wave, with the x-axis as distance, and y-axis as pressure. If the maximum pressure is at 2.5, is the average pressure is at 2.0, and if the pressure between the two are only rising, does this mean the answer is simply 0.5m?

I'm really grasping at straws here.
Elizabeth :uhh:

 

[jeroen]

First you need to understand how the cycle 'cycles'.

What sequence of pressures will you encounter as you go through the cycle?
Just name them high, low and medium.

Plot this sequence on a piece of paper.
Also draw the situation described in your post and plot th two distance-pressure pairs that are given.

 

[Elizabeth]

?

Thanks for the reply, and thanks for the suggestion.

I tried to think of a "plain" sinusoidal wave, with the high pressure as the peak, the medium as axis x across it, and the low, and the lowest peak. I'm thinking that the high peak is 2.5m, and that 2 is the medium(?), then the lowest must be 1.5m (?)

I know a cycle is a period, say from the high peak, to another high peak, so a cycle would be, from a high, medium, low, medium, back to high.

I'm not sure I'm making any sense, I feel like the answer is staring at me in the face, and I just can't make the connection.

Am I any closer?

 

[Dick]

You are making perfect sense. So what does your picture tell you the wavelength is?

 

[Elizabeth]

Thanks for the reply!

That would make it 2m.

High to Medium = 0.5
Medium to Low = 0.5
Low to Medium = 0.5
Medium to High = 0.5

That doesn't make much sense to me, it's the same as one of the numbers given in the question, and it's a pretty long wave length to boot!

PLUS, the question says, to assume it's rising only? rising only to what? 0.5m? That wouldn't make a complete cycle.

This is getting from bad to worse! I'm getting my british knickers in a right twist!
:tongue2:

 

[Dick]

For someone who has the right answer and picture, you are pretty nervous. The resemblance to one of the numbers in the question is a complete coincidence. The point to saying that it is rising only is that you could draw a shorter length wave that still has a 'medium' at 2m and a 'high' at 2.5m but it wouldn't be the first 'high'. Draw one.

 

[Elizabeth]

Okay... here it is!

Here's an attachment then! What do you think? Sorry, I wasn't sure how to embed into the reply.

Elizabeth

 

[Dick]

Approval seems to be slow in coming for your jpg. But since you seem to be less worried, I'm sure it will be fine!