Mechanical Waves. Transverse and Longitudinal Waves Transverse Longitudinal.

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Presentation transcript:

Mechanical Waves

Transverse and Longitudinal Waves Transverse Longitudinal

Transverse and Longitudinal

Transverse or Longitudinal?

Deriving the wave equation for a string

Deriving the wave equation (Cont.)

The wave equation (Skip)

Another Approach (Skip)

A more elegant proof (Skip):

Understanding the solutions

Waves Waves in general “Nice” waves (Sinusoidal waves)

Sinusoidal Waves We will focus on the sinusoidal waves. Why? Because they are nice and easy. Because all complicated wave forms can be create by adding up sinusoidal waves. (Fourier Analysis)

A wave moving to the right

Math

Wavelength λ

Period T and Frequency f

So how fast is the wave traveling?

Please remember this!!!

Transverse v and a As the wave moves to the right, each particle moves in the transverse direction (i.e. perpendicular to the direction of the wave). How to find their transverse velocity and acceleration?

Transverse v and a

Question

Find the maximum transverse speed

Question

What determines v ?

String tied at both ends L

Terminology

Pictures

The other two cases:

Energy transmission in waves (Skip)

More general (beats)