Frequency, Period and the Wave Equation
Recap:
Waves
Types
Longitudinal/Transverse
Review - Anatomy of a Wave
Investigation Period and Frequency : Pendulum
1) Create your pendulum using string, a marble and tape.
2) Tie a knot in the string at approximate distances of 10 cm, 20 cm and 30 cm from the marble.
3) One person hold the ruler to the desk and the pendulum to the ruler at the 10 cm knot. The other
person release it at a horizontal position, and time the pendulum. Record how many seconds it takes
to complete 10 full cycles. Do this 3 times and average your results.
Use the average amount of time to complete 10 cycles to determine two things:
a) How long does it take to complete 1 full cycle.
b) How many complete cycles will it completed in 1 second.
Complete Step 3 for lengths 20cm and 30 cm.
Question - Do you notice a relationship between the values you get for a and b, if so, what is it?
1 full cycle is called a Period T
The number of cycles per second is called Frequency f
Question - Can you write the relationship between T and f as an equation?
Period and Frequency
Frequency ( f )- the number of crests (or troughs) that pass a given point
(such as breaking on a shore) in a given time interval.
f = # of cycles
total time
Usually measures in events/ second
1 Hz = 1 cycle/second
Period: the shortest length of time that periodic motion repeats itself.
total time
T=
# of cycles
ie. 12 cycles in 2 seconds
ie. 12 cycles in 2 seconds
Example 1
A sound wave has a frequency of 262 Hz. What is the time between
crests?
Example 1
A sound wave has a frequency of 262 Hz. What is the time between
crests?
The Wave Equation
Deriving the Wave Equation
Remember from Grade 10 that v = ___
Δd
Δt
A travelling or continuous wave has as its source a continuous
oscillation.
The length of a full wave is called the wavelength, λ. The time needed
to produce one full wave is the period T.
Since the wave moves a distance of one wavelength during the time
interval of one period, the speed is give by:
Δd = λ
Δt =T
v=?
Important note:
The speed of a wave depends only on the
medium it is travelling through.
Example: Speed of Sound in water:
Temperature-(oC)
Speed of Sound
(m/s)
0
5
10
20
30
40
50
60
70
80
90
100
1,403
1,427
1,447
1,481
1,507
1,526
1,541
1,552
1,555
1,555
1,550
1,543
Example 2
A sound wave has a frequency of 262 Hz and a wavelength of 1.29m.
What is the speed of the wave?
Example 2
A sound wave has a frequency of 262 Hz and a wavelength of 1.29m.
What is the speed of the wave?
Sol'n
f = 262 Hz
= 262 s-1
λ = 1.29 m
v=?
v =fλ
= ( 262s-1)(1.29m)
= 337.98 m/s
=3.37 x 102 m/s
-3 sig figs
Example 3
A sound wave has a speed of 3.3 x 102 m/s and a frequency of
4.33 x 104 Hz. What is the wavelength of the wave?
7.6 x 10-3 m
orange book
Read pages 1-6
Complete pages 16-22
Engrade Quiz Due by
To take the quiz:
1) Log onto your engrade account
2) Go to your science class link
3) Click on "More"
4) Click on "Quizzes"
5) Click on "Waves" quiz.
6) Answer the questions. Use whatever resources you need to help you.
7) Check your answers.
8) Submit t he quiz.
If you will not have access to the Internet before the due date, see me
before that time to get a paper copy. Your paper copy will be due by end
of school day on the due date.