Waves

•
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)

•
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

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

•
Displacement, y, of a point on the wave is given by SHM equationy

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
)

•
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

)

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

)

•
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, y

A sin 2

( ft
 x

)
(c) the wavelength,
(d) the speed of the wave?
(All quantities are in S.I. units.)

•
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

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

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
)


•
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

•
Link
Now try making standing waves with rubber string, can you work out the speed of the wave?
Answer tutorial questions 7 to 10