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https://isaacphysics.org/questions/graph_interpreting_6_beats?board=55c55eb6-d53d-452f-8071-b65868d206db&stage=a_level
Working is attached below, I’m stuck on parts an and b and would really appreciate some help. I’m sure I’m making some wrong assumptions, I just don’t know what they are. Thank you in advance.

Youre sort of right although overly complex, but look at the time periods of the two sinusoids which are multiplied together (sum to product), so the solid and dashed lines, then f=1/T. Once you have those fm and Df, you can go back to f1 and f2 using the
f1+f2 = 2fm
f1-f2 = 2Df
which is easy to solve.
Note the =0s are wrong? Youve an expression and plotting the function. Youre not solving an equation.

Sorry to jump in but to clarify, are you saying to use the sun to angle formulae and equate that to 1/T in order to equate it to the freq, ie 1/0.05?

Here is my working. But I’m confused how to derive an equation for f_m, as the entire graph has the shape of the cos function, not the sin

These values are apparently wrong though. Could you show me where I went wrong?

What does wbf mean out of interest? I’ve seen you use it a couple of times

wbf, its less about writing equations down and more about interpreting the graph. By looking at the axis crossing times, it should be easy to see that the time period of cos (dashed curve) is T=0.2, so Df=1/T=5. Just do a similar interpretation of the solid line (sin) where you note that even though its being "squashed" by cos, the axis crossing times are unaffected, so T=.... and fm=..... Then f1=..., f2=....
Dont write down any maths.

wbf, its less about writing equations down and more about interpreting the graph. By looking at the axis crossing times, it should be easy to see that the time period of cos (dashed curve) is T=0.2, so Df=1/T=5. Just do a similar interpretation of the solid line (sin) where you note that even though its being "squashed" by cos, the axis crossing times are unaffected, so T=.... and fm=..... Then f1=..., f2=....
Dont write down any maths.

Without being funny. Its nbd (no big deal) but sometimes (often) the best way to solve maths problems is not to start writing down equations in the hope that algebra will save you, without having an idea of how things will work out.

I don't really understand how can you get fm knowing T, T=0.2s, but how are you supposed to get fm? And how is it going to help you, does it have anything to do with fm=(f_1+f_2)/2 so if you know fm and you know f_1, you therefore know f_2.? Essentially my question is: how do you get fm?

cos is effective the dashed envelope and sin is effectively the (squashed) solid curve from which you can read off the time period and hence fm=1/T
The whole point of the question is that its hard to read off the time periods/frequencies when you have
sin() + sin()
however, if you use the sum to product identity and transform it into
cos()sin()
it should be easy as the cos is the envelope and sin is the fast oscillations within the envelope (hint 4).