Periodic Wave formula; need explanation?

I was listening to Quantum Mechanics lecture and there were wave explanation; to be exact it is periodic wave ..

its formula is v (speed) = lambda (wavelength) X f (frequency cycles/second)

the professor said that if for example wavelength is shorter wave, that means the frequency is becoming higher .. and if wavelength is longer wave, that means the frequency is becoming lower ...

I don't get it, I thought that if we have an object which has many cycles per second such as 50 c/s, then it has much more opportunity than the 30 c/s to reach as far place as I know...

please someone could explain what does professor means?

Answer

Imagine a wave that advances 10 meters per second.

if every second a wave crashes on the shore, the frequence is one per second (1 herz) the wavelength is then 10 meters since each second the wave advanced 10 meters and therefore the waves are 10 meters apart.

If we halve the wavelength (the wave still advances at 10 meters per second) then the waves are 5 meters apart. if waves 5 meters apart advance at 10 meters per second then 2 waves will crash on the shore per second. This means that the frequency of waves has doubled.

Conclusion : if the speed of a wave in an environment is constant, then doubling the frequency is equivalent to dividing wavelength by two.

Constant = frequency * wavelength

for electromagnetic waves : speed of light = frequency * wavelength