the wave equation: v = fλ

The wave equation: v = fλWavelength =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.

Transverse Wave Longitudinal Wave

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/simulations/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?

How does the guitar player tune the guitar? v = [F/(m/L)]

• So, by tightening the string… what happens to the Force due to tension?

• Force due to tension increases.

• What happens to the speed of the wave?

• Therefore, the speed of the wave increases.

• What happens to the frequency of that wave?

• Therefore, since 𝝺 = v/f, if v increases then f increases while 𝝺 is constant.

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.)

•The speed of a wave is affected by the properties of the material or medium through which the wave travels.

•The speed of a wave also depends on the type of wave… sound wave, electromagnetic wave, water wave, seismic wave, etc.

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 20o 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 oC.

• 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’llneed to go here when doing your homework).

Found on Page 482

in your textbook

Electromagnetic Waves (NOT sound waves)…All electromagnetic waves (not sound waves) move at a remarkable speed of 3.0 X 108 m/s in a vacuum. Electromagnetic waves do not need a medium to travel through… unlike sounds waves which require a medium.

• E-M waves: Radio, Infrared Radiation, X-rays, Ultraviolet Radiation, Microwave, Light, Gamma…

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.

Power & Sound Intensity of a Sound Wave

•Power of a wave: the amount of energy transported each second. This energy can do work, such

as vibrate an ear drum or cause damage to buildings, as in a sonic boom.

•P = W/Δt = nrg/Δt• Units: Joules/second, or Watts!

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

• I = P/A• units: Watts/meter2 = W/m2

• 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 = IA (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.

Decibels=a measurement which compares two sound intensities, I/Io. I = the intensity of the sound, Io= reference level to which I is being compared. Usually, Io=the threshold of human hearing (lowest intensity perceived) = 1x10-12 W/m2 = Io

• We call that apparent loudness the intensity level, ß, measured in decibels (dB) and we can find it if you know the intensity in Joules per second per square meter (or W/m2) using the following logarithmic equation:

• ß = 10 log (I / Io)where Io is usually the softest sound the human ear can distinguish, at 1x10-12 W/m2 or J/s/m2.

• Notice that if I = 1x10-12 W/m2, then ß = 0 dB (decibels).

• Other samples of loudness are normal conversation, about 60 dB, whispering, about 15 dB, and loud music, about 120 dB.

Every increase in 10 dB results in a 10 times increase in

Power of that sound wave!

Decibels

•Roughly speaking…

•each 10 dB increase in sound level corresponds to a "doubling of subjective loudness“ and a 10-times increase in the intensity and therefore, power of that sound.

For example, jackhammer noise at 110 dB would typically be judged to be 2 x 2 x 2 x 2 = 24 = 16 times as loud, and 104 = 10,000 times more powerful as the inside of a car at 70 dB.

Doppler EffectAs the Fire Truck approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch. As the Fire Truck recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the Fire Truck is coming nearer or speeding away. If you could measure the rate of change of pitch, you could also estimate the Fire Truck's speed.

Either the source of sound could be moving, or the observer of the sound

could be moving… Doppler Effect is still observed in either case.

• http://www.youtube.com/watch?v=a3RfULw7aAY

Sonic Boom!

http://www.sky-flash.com/boom.htm

http://www.youtube.com/watch?v=-d9A2oq1N38

https://www.youtube.com/watch?v=gWGLAAYdbbc

Everything About Waves

• http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm

• http://www.youtube.com/watch?v=-Zu5SGllmwc&feature=related