Today’s Topic: Wave Speed – Part 2

Learning Goal:

SWBAT calculate the speed in which waves travel.

Please turn in your labs and SHM worksheets. Make a pile on my desk up here.

Then clear off your table for a small quiz.

HomeworkDue Today (May 28th):

Complete the Pendulum Lab

Complete the Simple Harmonic Motion Worksheet

Due Wednesday, 6/3:

Complete the Wave Speed Worksheet

Wave MotionSo far, we have seen the motion of a

pendulum and a mass-spring, and we’re very familiar with its motion.

If we were to fill a pendulum bob with sand and have it oscillate on the table, what shape would the sand make?

What if we had it oscillate over a moving conveyer belt?

Anatomy of a Wave

The high points at the top of the wave are called crests.

Anatomy of a Wave

The low points at the bottom of the wave are called troughs.

Anatomy of a Wave

The distance from crest-to-crest, trough-to-trough, or any two adjacent points is called the wavelength (λ).

Wavelengths are measured in meters.

λ

λ

λ

Anatomy of a Wave

The wave moves the full length of the wavelength before is repeats again.

λ λ

Anatomy of a Wave

The gray line between the crest and trough notes the equilibrium position.

Anatomy of a Wave

The distance from the equilibrium position to the crest (or trough) is known as the amplitude. (A)

Amplitude is also measured in meters.

Speed of Waves

Remind me again – what does frequency tell you about the motion of a wave?

How many waves occur per second

If we also know how long a wave is, we can determine how quickly a wave is moving!

RecapLight and sound are two common waves

that we inadvertently interact with on a daily basis.

What does a sound wave with a small amplitude sound like?

What does a sound wave with a large amplitude sound like?

RecapWhat about light? What would a light

wave with a small amplitude look like?

Large amplitude?

Amplitude affectshow intense thewave is. (Thinkwaves on a beach)

Amplitude vs Frequency

Is it possible to have a large amplitude and a large frequency?

Let's See

Amplitude and Frequency are variables that are independent of each other.

FrequencyRecall – what does the frequency of a

wave measure?

How does this translate into sound – what is happening when we hear a wave with a frequency of 30 Hz?The wave is completing 30 complete cycles in one second.

What about 10,000 Hz?

FrequencyWhat does this all sound like though?

Let’s have a listen.

Sound FrequenciesHumans commonly hear between 20 Hz

to 20 kHz. Most sensitive to 2 – 5 kHz.

Note: YouTube videos only encode up to 18,000 Hz.

Other creatures have different hearing ranges.

Fun Fact:The censor bleep is a 1,000 Hz tone.That’s $!@%ing cool!

Light FrequenciesAs for light, our eyes can see

frequencies in the 430 – 790 THz range (Tera – 1012)

Physicists normally refer to the color spectrum in terms of their wavelength.

The human eye responds to wavelengths from about 390 nm to 700 nm.

700 nm = red390 nm = violet

Light FrequenciesThe colors we see are a part of the

visible spectrum.

As Fast As a Speeding Bullet?

How do we calculate how fast a wave is travelling?

What factors do we know about waves at this point?

Wavelength, Amplitude, Frequency, etc.

Let’s think though…

Wave Speed CalculationLet’s say you’re standing at a dock.

If you know the distance between the crests on a wave (wavelength) and you count the number of waves that pass by every second (frequency), then you can calculate the distance the wave travels each second.

Wave Speed

To calculate the speed of a wave: multiply the wavelength by the frequency.

Wave SpeedThe formula for wave speed is:

v = λ • f

Wave Speed = Wavelength • Frequency[m/s]

vλ f

[m] [Hz]

Wave Speed

If the crest-to-crest distance between waves is 4 m long, and 3 crests pass by a stationary point each second, how fast are the waves traveling?

(4 m * 3 crests per second) = 12 m/s

Example Problem

Gob throws a letter into the ocean (not seen successfully above).

If the crest-to-crest distance of the waves is 1.25 m, and one wave passes by every 2 seconds, how fast are the waves travelling?

Example Problem

If Gob throws the letter a distance of 7 m into the ocean, how long will it take for the letter to return to Gob?

Speed of Waves

Waves move – some faster than others.

Where have seen and heard this before?

Thunderstorms!

Speed of SoundDepending on the composition of the air

(humidity, temperature) the speed of sound in air changes.

In dry air at 20 ºC (68 ºF), sound travels at approximately 343 m/s. (1,127 ft/s)

The formula for the speed of sound is:

vair = 331 m/s + 0.6•T

Sample ProblemOn a 20 °C day, two friends shout at

each other in an open field.

If it takes 0.73 seconds to hear each other, how far away are they from each other?

Sample ProblemA person standing at the edge of the

Grand Canyon on a 25 °C day shouts down to the bottom.

If the floor of the canyon is 700 m below, how long will it take for them to hear their echo?

Speed of LightLight, and all electromagnetic radiation,

travels at the same speed.

Light, and all electromagnetic radiation, travels at approximately 3x108 m/s. This is called the speed of light (c).

To be more exact, light travels at 299,792,458 m/s, but we’re never going to use that value. (Off by 207,542 m/s)