{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mechanical_waves_travel

# mechanical_waves_travel - MECHANICAL WAVES(TRAVELLING We...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MECHANICAL WAVES (TRAVELLING) We begin our discussion of the wave phenomenon by considering waves in matter. The simplest deﬁnition of a wave is to call it a traveling disturbance (or equivalently, deviation from equilibrium). For instance, if you drop a stone on the surface of an undisturbed body of water you can watch the “disturbance” traveling radially out of the “point” of contact. Formally, we can “construct” a wave in several steps. For simplicity, we take a wave traveling along x—axis. Step 1. We need a disturbance D. Step 2. D must be a function of x. Step 3. D must also be a function of t. Step 4. If x and t appear in the function in the combinations (x Trvt) the disturbance D cannot be stationary. It must travel along x with speed v. Further, (x—vt) implies v = vﬂtravel in+ ivex — direction] —) (x+vt) implies v = —v£[travel in— we): — direction] ._) EXERCIZE: Put D = A(x — If)2 and show that “parabola” travels. Periodic Waves The simplest wave is when (x-vt) appears in a sin or cos function. D = sin (x—vt) But this equation is not justiﬁed. First, since D is a disturbance it must have dimensions so we need D: A Sin(x— vt) Where A has the dimensions of D. Next, argument of Sin cannot have dimensions, so we need (x— vt) /l D=A Sin v Where 1 is alength. Since A has dimension of (l/Time), put is: % 275x 2m Next, introduce a phase angle Q and we get D = A Sin(7— 7+ Q) as the most general periodic wave. Note that 27: has been put in, as we know repeat angle for Sin. If you put Q = 7? you recover the Equation in some books. . 2m 27m) D— ASm[ T — A As shown in class xt = Repeat Distance= wavelength . 1 T = perlod, E = f (frequency) And v = ftf 27\$ Next, deﬁne k = 7 (wave vector) 0) = 27tf (angular frequency) a) = vk And we can write D = A Sin (kx — wt + Q) for any periodic wave traveling a long +z've x—axis A x H a) with velocity v I 4, Similarly, D = A Sin (be + wt + Q) is any periodic wave along —ive x-axis with ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

mechanical_waves_travel - MECHANICAL WAVES(TRAVELLING We...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online