A single wavelength L = VT where V is the speed of the wave and T is the time to travel one wavelength, it's called the period. We often call one wavelength a cycle.

So in the image, we see a wave start at X. It waves up then down and back up again. Its amplitude is where it reaches max height and min height from the line between X and Y. And where is crosses the line a second time, that starts a second wave. So that first wave is replicated between X and Y three times.

In other words, there are three lengths of that one wave shape. Or three cycles. And as X to Y is S = 4.8 m and N = 3 cycles/lengths, each length L = S/N = 4.8/3 = 1.6 m.

Finally it takes T = 6 s to travel N = 3 wavelengths (cycles); so the frequency F = N/T = 3/6 = 1/2 cycles/sec. ANS.

You can see this in the image. If each 1/2 cycle takes a second, count up the number of half cycles. You get 6 half cycles. And at 1 second per, that's 6 seconds for the entire X to Y length. Which is what was given.

A cycle is a complete sinusoidal wave. In this case, hitting the broken line on the upswing.

There are 3 complete cycles in your illustration.

After a complete cycle, the numeric values repeat, e.g.; starting at zero and increasing.

Think of the sine function from 0° to 360°.

Don't forget your engineering units!

1/second = 1 s^-1 = 1 Hz.

Define Crest In Physics

A cycle includes both the crest and the trough. But whenever I have trouble remembering it, I think of it this way: If I were starting at the very beginning (the far left), how far would I have to move to the right in order for the pattern to EXACTLY repeat? You can see that at the left edge of the graph, the height is at zero and the graph is heading "uphill". Now move to the right to the first place where this condition repeats (that's about 1/3 of the way across this graph). That's one cycle (a.k.a. one "wavelength").

Frequency is just the number of cycles in one second. However its unit was changed to Hertz (Hz) within my lifetime. A cycle is just that. Its the time taken for the oscillation to come back to the same amplitude for the second time (Y in your graph?) and the whole cycle begins again with the same positive going amplitude. If distance is involved then the wavelength is the distance travelled by one cycle (I assume that is X in your graph).

Only 3 cycles here. It is a sine wave. One cycle of the wave is 360 degrees. Your diagram starts at 0 degrees. Upper peak is 90 degrees, crossing zero line is 180 degrees, negative maximum is 270 degrees, back to zero at 360 degrees.

Note that a cosine wave starts at +90, goes to 0, then to -90 then to 0 then to +90 again total is still 360 degrees. You can do the math using this knowledge

Correction: The number of cycles is determined by the number of crests, but we must define, crest, a crest is in both upward and downward direction ( referenced as the positive peak and the negative peak of a transverse wave. ) each cycle must have one positive crest ( peak ) and one negative crest ( peak ), so count the number of both crests and divide by the number,(should be 2), to determine the number of cycles across the shown image (should be 3. the number of cycles). Next, we need the determine the length of time across the image, shown ( 6.0 second of time, located in foot note. ). Now that we have the length of time we can apply your original equation of ( frequency =number of cycles / time ). This will only give you part of what was suggested in the image, the frequency.

Note: Your question about the crests and troughs, you can use either, but you need only to use one, or the other.

1/2 cycle/ sec or .5 hertz. As frequency now is measured in Hertz.

Try formula of wavelength

A cycle is always peak to peak or trough to trough. Think if this as a trigonometric function. Going through

a cycle means that you have to go through 2PI

There're 3 cycles my friend, in one oscillation we count crest and through as single oscillation or cycle.