Wave Problem: Length & Velocity

[Turbo Math]

[SOLVED] Wave problem

Homework Statement

a small stone fell into alake causing 40 waves after 4 seconeds, if the radius of the outter circle is 1.6 meters, find the length of the occurred wave and its velocity

Homework Equations

The Attempt at a Solution

well i got two different solutions so far cause i couldn't determine what exactly was meant by (r=1.6m & length of the occurred wave):

1- f = 10 Hz

lambda/4 = 1.6
lambda = 6.4 m

v = lambda.f
= 6.4 × 10
= 64 m/s

========================

2- v = x/t

x = 2pi.r
= 10 m

v = 10/4
= 2.5 m/s (oO)

 

[Doc Al]

Neither approach is good. Instead, picture what's going on. The waves travel outward from the center. The outer radius tells you how far the first wave traveled in the given time. Use that to find the speed of the wave.

Also, you have 40 waves (and thus 40 wavelengths) stretched out over that radius. How big is each wavelength if 40 of them add to the outer radius?

 

[Turbo Math]

aha! so:

v = 1.6/4
= 0.4 m/s

and...

lambda = 0.4/10
= 25 m

i hope i got at least closer ^^

 

[Doc Al]

aha! so:

v = 1.6/4
= 0.4 m/s

Good!

and...

lambda = 0.4/10
= 25 m

Not good. If 40 wavelengths span 1.6 m, how can each wavelength be 25 m?

 

[Turbo Math]

I don't think i get it

is it that i reversed the final result 25->0.04 (this happens all the time and its really annoying) or i simply skipped a step that i can't figure?

 

[Doc Al]

is it that i reversed the final result 25->0.04 (this happens all the time and its really annoying) or i simply skipped a step that i can't figure?

That must have been what you did. You wrote .4/10 (which is correct), but you reversed the answer.

What I would have done is this:
40 Wavelengths = 1.6 m
1 Wavelength = (1.6 m)/40 = 0.04 m

 

[Turbo Math]

I knew it

the problem was that i haven't known that the wavelengths make out the radius as this is my first encouter with circular waves

anyways thanks a lot Doc Al cya