The wave equation: v = fλ, Lecture notes of Particle Physics

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The wave equation: v = fλ

Wavelength =𝛌= the length of one wave (m) Frequency = f =

of cycles

completed per second (Hz) V = speed of wave (m/s) crest trough A=Amplitude

1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.

How is a guitar made to create

different notes/pitches/frequencies?

• A wave’s speed, v, traveling through a string (via a transverse wave) is affected by…
• the tension (F) in the spring, and
• the mass (m) per unit length (L) of the string, also called the linear density, m/L, and follow this relationship…
• v =  [F/(m/L)] http://phet.colorado.edu/si mulations/sims.php?sim=W ave_on_a_String

How does the guitar player tune the guitar?

v =  [F/(m/L)]

• Tightening or loosening the string changes the tension in the string which changes the speed of the wave in the string which changes the frequency of that wave (and not the wavelength—the wave still has that same confined length).
• So, by tightening the string… what happens to the Force due to tension?
• What happens to the speed of the wave?
• What happens to the frequency of that wave?

Think about this… Are all guitar strings made of the same m/L ratio string (same thickness)? v =  [F/(m/L)] What if you double the mass to length ratio of the string you are using to play guitar? i.e., Are guitar strings all the same “thickness”— mass to length ratio? What happens to the speed of the wave traveling through a string with twice the m/L ratio? What happens to the wavelength? What happens to the frequency of the wave generated from that string with “twice the thickness?”

Think about this… Are all guitar strings made of the same m/L ratio string (same thickness)? v =  [F/(m/L)]

• What if you double the mass to length ratio of the string you are using to play guitar? (What happens to the speed of the wave traveling through a string with twice the m/L ratio?)
• The speed decreases by √(½).
• What happens to the wavelength?
• The wavelength is not changing… 𝝺 = v/f
• What happens to the frequency of the wave generated from that string with “twice the thickness?”
• Therefore, while wavelength stays constant, if the speed decreases by √(½), then frequency decreases by √(½). ( And…√(½) = 1/√2.)

Sound Waves…

• Fun with sulfur hexafluoride http://www.youtube.com/watch?v=V2FR6-gEwjU
• Sound waves travel at 343 m/s through air

at an air temperature of 20

o

C (slower if air

temp is lower, faster if air temp is higher).

• V sound in air

=331 m/s + (0.6 m/s/

o

C)T

• T is temperature of air through which the

sound wave is traveling. T is measured in

o

C.

• Sound waves travel at different speeds

depending on the medium… Faster in solids,

then liquids, then slowest through gasses.

• See Table 15.1 on pg. 482 in your textbook (below) for the speed of sound in different media (you’ll need to go here when doing your homework). Found on Page 482 in your textbook

A sound wave is a series of alternating

condensations and rarefactions; each

molecule executes Simple Harmonic

Motion about a fixed location.

A sound wave is a series of alternating condensations and rarefactions; each molecule executes Simple Harmonic Motion about a fixed location.

• Sound Intensity, I: the sound power that passes perpendicularly through a surface divided by the area of that surface.
• I = P 

/A

• units: Watts/meter 2 = W/m 2
• As you move away from a sound source, the same power is spread over a greater and greater area causing a decrease in intensity (quieter).
• P 

= IA (I & A are inversely

proportional)

• The scale used to measure and compare the loudness of sound is called the decibel scale.
• The decibel is named after Alexander Graham Bell who did a lot of work in the area of sound and loudness.
• He discovered that to obtain a sound that seems twice as loud as another sound, the intensity (how much sound energy per unit area per second hits the eardrum) of the sound must be multiplied by 10.

Every increase in 10 dB results in a

10 times increase in

Power of that sound wave!

Decibels