Waves
-Types of waves
- Mechanical waves eg sound waves, water waves, air waves,
- Electromagnetic waves - electromagnetic spectrum eg radio, light, microwaves,
infrared, x rays, gamma rays, UV, etc
(radioactivity- disintegration of large unable atoms into smaller stable ones, releasing
energy(gamma rays), particles (beta and alpha)
Types of wave motion
There are two types,
- transverse and
- longitudinal.
In a transverse wave, the direction of the disturbance is at right angles to the direction of
travel of the wave eg all EM waves
In a progressive longitudinal wave the particles of the transmitting medium vibrate to and
fro along the same line as (parallel to) that in which the wave is traveling and not at right
angles to it as in a transverse wave eg sound waves
C - compression
R - rarefaction
General Wave Properties
Terms used to describe waves can be explained with the aid of a displacement–distance graph
a) Wavelength
The wavelength of a wave, represented by the Greek letter λ (‘lambda’), is the distance
between successive crests.or troughs
In longitudinal waves, the wavelength is the distance between successive compressions or
RAREFACTIONS
b) Frequency
The frequency f is the number of complete waves generated per second. If the end of a rope is
moved up and down twice in a second, two waves are produced in this time. or 2 hertz (2 Hz;
the hertz being the unit of frequency), which is the same as the frequency of the movement of
the end of the rope.
That is, the frequencies of the wave and its source are equal
The frequency of a wave is also the number of crests passing a chosen point per second.
c) Speed
The speed v of the wave is the distance moved in the direction of travel of the wave by a crest
or any point on the wave in 1 second.
d) Amplitude
The amplitude a is the height of a crest or the depth of a trough measured from the undisturbed
position of what is carrying the wave, such as a rope
The wave equation
The faster the end of a rope is vibrated, the shorter the wavelength of the wave produced. That
is, the higher the frequency of a wave, the smaller its wavelength. There is a useful connection
between f, λ and v, which is true for all types of wave.
Suppose waves of wavelength λ = 20 cm travel on a long rope and three crests pass a certain
point every second. The frequency f = 3 Hz. If Figure 25.3 represents this wave motion then, if
crest A is at P at a particular time, 1 second later it will be at Q, a distance from P of three
wavelengths, i.e. 3 × 20 = 60 cm. The speed of the wave is v = 60 cm per second (60 cm/s),
obtained by multiplying f by λ. Hence
speed of wave = frequency × wavelength or v = f λ
This is called the wave speed equation
From the wave equation, if speed of the wave is constant, frequency is inversely proportional to
wavelength
This can be presented graphically as shown below.
Example
The figure below shows a displacement-time graph of a wave travelling at 2500 cms-1
Determine for the wave:
a) Amplitude
Solution
A = maximum displacement from mean position
=3cm OR 0.03m in SI units
b) Periodic time (Period,T- it’s the time taken by a particle to complete one oscillation. SI unit of
period is the second(s))
Solution
T=(9-1) x 10s-3s
=8x10-3s
c) Frequency
Solution
d) wavelength
Work to do
1. The lines in the figure below are crests of straight ripples.
a What is the wavelength of the ripples?
=0.05m 1 cm
b If 5 seconds ago ripple A occupied the position now occupied by ripple F, what is the
frequency of the ripples?
f = waves per second
f = 5 waves / 5 sec = 1 wave per sec = 1 Hz
c What is the speed of the ripples?
v=fλ
v = 1 x 1 = 1 cms-1
2. Name two types of progressive wave motion.
Transverse and longitudinal✔
3. The diagram shows a student standing midway between a bell tower and a steep
mountainside
The bell rings once, but the student hears two rings separated by a short time interval.
a) Explain why the student hears two rings.
The sound waves of the bell at the bell tower is reflected which is called an echo thus the
students hears two rings separated by a short time interval
b) State which of the sounds is louder, and why
The original sound by the bell since the echoed sound starts to faded as time moves thus
making the echo not being louder enough
c)Sound in that region travels at 330 m/s.
(i) Calculate the time interval between the bell ringing and the student hearing it for the first time.
1
T= 𝑓
1/990 x 330m/s
(ii) Calculate the time interval between the bell ringing and the student hearing it for the second
time.
(iii) Calculate the time interval between the two sounds
4. A vibrator sends out 12 ripples per second across a ripple tank. The ripples are observed
to be 5cm apart. Find the velocity of the ripples.
5. A water wave travels 2m in 5 seconds. If the frequency of the wave is 10Hz, calculate
the:
I. Speed of the wave
II. Wave length of the wave
6. The diagram below shows a displacement-time graph for a certain wave
I. How many oscillations are shown above?
II. Calculate the frequency of the wave
III. Calculate the periodic time of the wave
7. Electromagnetic waves travels at a velocity of 3.0x108ms-1 in air, calculate the
wavelength in air of radio waves transmitted at a frequency of 200MHz.
8. Wave ripples are caused to travel across the surface of a shallow tank by means of a
suitable straight vibrator. The distance between successive crests is 6.0cm and the
waves travel 50.4cm in3.6 seconds. Calculate:
I. The wavelength
II. Velocity
III. Frequency of the vibrator.
9. Water waves are observed as they pass a fixed point at a rate of 30 crests per minute. A
particular wave crest takes 2 seconds to travel between two points 6m apart. Determine:
I. The frequency
II. The wavelength
10. Calculate the wavelength of the KBC FM radio wave transmitted at a frequency of
95.6MHz
11. The audible frequency range for a certain person is between 30Hz and 16500Hz.
Determine the largest wavelength of sound in air the person can detect (speed of sound
in air is 333m/s)
12. The figure below represents a displacement-time graph for a wave.
I. Determine the frequency of the wave
`II. Sketch on the same axes the displacement-time graph of the wave of same
frequency but 1800 out of phase and with smaller amplitude.
