the physics of waves wave math 9-12 science std: phys 4b

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


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?


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






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






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

the physics of waves wave math 9-12 science std: phys 4b

Documents