the physics of waves wave math 9-12 science std: phys 4b
TRANSCRIPT
The Physics of Waves
Wave Math
9-12 Science Std: Phys 4b
Did you notice…… Did you know that the things we measured work together?
The frequency, the wavelength and the speed of the waves depend on each other
There is a math formula that shows how they work together
velocity = frequency x wavelength
or (math equation time)
v = f x λ
So how does this work? Remember the demonstration where we made standing waves
You started out slow – making a standing wave that had 2 crests and 3 nodes
measure the wavelength
count the number of times your hand moved to find
the frequency
So how does this work? Remember the demonstration where we made standing waves
Then you went faster, making a standing wave that had 3 crests and 4 nodes
Did you notice that the wavelength got
shorter?
And the number of times your hand moved went up so the frequency went up?
So how does this work? Remember the demonstration where we made standing waves
Finally, you went the fastest and made a standing wave with 4 crests and 5 nodes
And the wavelength got even shorter?
And the frequency went even higher?
So how does this work? In fact, if the frequency doubled (2x)…..
The wavelength was cut in ½
v = f x λ We can see this in the formula:
If the velocity stays
constant
Every time the
frequency goes up
The wavelength goes down
Here’s an easy way to work it… Remember the “Formula Triangle”
In the formula triangle, one side of the formula goes up in the top
The other side of the formula goes on the bottom of the triangle with one part in each box
Here’s an easy way to work it… Remember the “Formula Triangle”
The lower section items are multiplied together
And they equal the top section
X
=
Here’s an easy way to work it… So for the formula v = f x λ
The two items on the bottom are multiplied together
V
f λX
And they equal the top item
=
Here’s an easy way to work it… If you are missing one of the lower parts
You can divide the top part by the lower part you have
V
f λ=
And they equal the missing bottom item
∕
An example with numbers…. If the frequency is 5hz and the wavelength is 0.75m
What is the speed of the wave?
V
f λ
Use the equation v = fλ and fill in the triangle
Fill in the numbers we know…..
5 hz 0.75m
And using the triangle, solve for what we don’t know
X
V = 5hz x 0.75m
V = 3.75 m/s
hz = 1/sec
3.75 m/s
7.0 m/s
How about another…. If the wavelength is 1.0m and the speed is 7 m/s
What is the frequency of the wave?
V
f λ
Use the equation v = fλ and fill in the triangle
Fill in the numbers we know…..
7 hz 1.0m
And using the triangle, solve for what we don’t know
/ f = 7.0 1/s
hz = 1/sec
f = 7.0m/s / 1.0m
So why don’t you try some….. Remember to use the formula triangle to help you
A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave?
A slinky has a wave speed of 10 m/s. You
see a wavelength of 150 cm. What is the
frequency of the wave?
Work together at your tables and we will check your answers in a little bit
f λ
V
So why don’t you try some….. Remember to use the formula triangle to help you
A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave?
A slinky has a wave speed of 10 m/s. You
see a wavelength of 150 cm. What is the
frequency of the wave?
Work together at your tables and we will check your answers in a little bit
f λ
VV = fλ
V = (200hz)(0.5m)
V = 100 m/s
X
So why don’t you try some….. Remember to use the formula triangle to help you
A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave?
A slinky has a wave speed of 10 m/s. You
see a wavelength of 150 cm. What is the
frequency of the wave?
f λ
VV = fλ
V = (200hz)(0.5m)
V = 100 m/s
X/
f = v/λ
f = (10m/s)/(1.5m)
f = 6.66 hz
When we made waves We made 2 types of waves:
Transverse waves
These are waves that move back and forth perpendicular to the way the wave is traveling
Longitudinal waves
Also called compression waves, these move in the same direction as the wave is traveling
When we made waves We made 2 types of waves:
We looked at the parts of a wave
Crest Trough Amplitude
Wavelength
And we counted the frequency Remember that the frequency is the count of how many times a wavelength goes by in one time interval (normally, the # of crests per second)
We even talked about the period
The period is a measure of the amount of time it takes for one wavelength to go by
We made single pulses and standing waves
We even measured the standing waves and started doing some math with what we measured