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Does the Middle C have a longer or shorter wavelength in water than in air and why?

Middle C has a speed of 1500 m/s in water and 340 m/s in air.

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)

Concept: The frequency won't change in water or in air.

Since wavelength x frequency = speed, wavelength is proportional to speed.

So, Middle C has a longer wavelength in water than in air.

Andrew L. | Educating, One Mind at a Time!Educating, One Mind at a Time!
5.0 5.0 (208 lesson ratings) (208)

So it turns out that there are really only 2 things that affect the velocity of a wave in a medium.

  • The medium's change in shape (elasticity)
  • The medium's change in motion (inertia)

This illustrates a pretty interesting concept of wave physics.  Whether a turtle is crawling or a jet is speeding long as we are in a constant medium, the velocity of the sound wave it produces will always be the EXACT SAME!!

Now, as we change mediums something interesting happens.  Our frequency stays exactly the same, however our speed still goes down (if it didn't, we would be violating an energy law).  

If we want to change the speed of the wave without manipulating the frequency...from v=(wavelength)(frequency), it becomes apparent that the wavelength is altered more specifically it becomes longer in water and the frequency is held constant.  Pretty crazy! 

That means, if you play a middle C underwater it will sound exactly the same as a middle C above water, but there will be a longer delay time until to hear the sound.  

Hope that helps!