So, is the frequency of the wave affected by the change in velocity?If so, how?

[SEZHUR]

I've got a sinking feeling that the answer to this question is blatantly obvious, but here goes:
If a wave of velocity v, frequency f and wavelength $$\lambda$$ travels through a medium whose density is inversely proportional to distance, such that the further the wave travels the greater the velocity of wave, in what manner do f and $$\lambda$$ change?

Put more simply, if neither the wavelength nor the frequency is held constant and the wave speed increases, how do the wavelength and the frequency change in order to accomadate the change in velocity.

My guess at an answer is that each changes as the square root of the change in the velocity
Eg. 2v=$$\sqrt{2}$$$$\lambda$$$$\sqrt{2}$$f

Thanks for your time

Ps. How do i get the latex commands to work without them jumping down a line?

 

[tiny-tim]

Welcome to PF!

Hi SEZHUR! Welcome to PF!

(write "itex" rather than "tex", and it won't keep starting a new line …)

If a wave of velocity v, frequency f and wavelength $\lambda$ travels through a medium whose density is inversely proportional to distance, such that the further the wave travels the greater the velocity of wave, in what manner do f and $\lambda$ change?

The frequency stays the same.

 

[SEZHUR]

Thanks for your response and sorry for the delay in mine.
I spoke to my tutors and they gave the same response you did; upon pushing for a reason it became apparent that the real reason why frequency remains constant is locked up a few levels above me so for the moment I'm happy to believe it based on energy conservation (if frequency changes then so does energy...)

Finally, let me test out your advice for latex...
v = $\lambda$f

Thanks

 

[filza]

frequency remains constant because it is only dependent on the source of vibration and not on the medium it travels, i guess!

 

[tiny-tim]

Hi SEZHUR!

Look at two molecules on either side of an interface, almost touching each other …

they must have the same frequency as each other, otherwise you'd have a continuous sliding earthquake at the interface, wouldn't you?

(And it's the same even if the medium changes gradually rather than suddenly.)