Advanced Higher Physics

Waves

Wave Properties 1

• • • • • Displacement, y (unit depends on wave) Wavelength, λ (m) Velocity, v  v = f λ (ms -1 ) Period, T  T = 1 / f (s) Frequency, f  f = n / t (Hz) A • Amplitude, A (unit depends on wave)

Types of Wave

• Transverse- displacement is perpendicular to direction of motion  e.g. water waves, e-m waves, wave on string, seismic ‘S’ waves • Longitudinal - displacement is parallel to direction of motion  e.g. sound waves, seismic ‘P’ waves Link

Wave Properties 2

• • • Intensity – (Irradiance)  I = P / A (W m -2 ) Coherence  Wave on right have equal wavelength, frequency and amplitude Phase  Waves are out of phase

Travelling Wave Equation

• • • Displacement, y, of a point on the wave is given by SHM equation-

y



A

sin( 2 

ft

) The wave travels at speed

v

from the source, so at a displacement,

x

, the disturbance arrives after a time -

t



x v

So at point x, the wave has the equation -

y



A

sin 2 

f

(

t



x

)

v

Travelling Wave Equation

• We can rearrange this if we substitute for

v = f λ y



A

sin 2 

f

(

t

 

y y

 

A A

sin sin 2 2   ( (

ft ft

  

x

)

v fx v fx

) )

f

 

y



A

sin 2  (

ft



x

 )

Travelling Wave Equation

y



A

sin 2  (

ft



x

 ) N.B. we are taking the sine of the angle (ft x/λ) - this is expressed in

radians

. Also note that at t = 0, y = 0 at point x = 0.

If the wave is travelling in the opposite direction (i.e. right to left) its equation will be -

y



A

sin 2  (

ft



x

 )

Example 1

• • A periodic wave travelling in the

x

-direction is described by the equation

y = 0.2 sin (4



t - 0.1x)

What are (a) the amplitude, (b) the frequency, (c) the wavelength, (d) the speed of the wave?

y



A

sin 2  (

ft



x

 ) (All quantities are in S.I. units.)

Example 2

• For the previous wave,

y = 0.2 sin (4



t - 0.1x)

Calculate the displacement of the medium, y, caused by the wave at a point where

x

= 25 m when the time

t

= 0.30 s.

Now do tutorial questions 1 to 6

Intensity

The intensity of a wave is directly proportional to the square of its amplitude.

Intensity



A

2

Transverse Speed and Acceleration

y



A

sin 2 

f

(

t



x

)

v

Differentiate with respect to time to find velocity and acceleration in the y direction.

Phase Difference

x p The phase difference between a particle at point p a distance x from the origin and the origin.

 = 2  x  The phase difference between any two points is  = 2  (x 2 – x 1 ) 

Stationary Waves

• • Two waves with equal amplitude and wavelengths travelling in opposite directions.

Phase change of  radians at surface.

Nodes – points where amplitude is always zero.

Antinodes – points where there is maximum change in amplitude.

Distance between nodes is  /2 link

Experiment

• Link Now try making standing waves with rubber string, can you work out the speed of the wave?

Answer tutorial questions 7 to 10

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