Dec. 8 – Resonance and Characteristics of Sound

Handout

• Frequency of standing waves 

Last week we discussed how wavelength of a standing wave is related to the length of the spring.  This handout explains how the same length is related to frequency.  The important thing to take away is that all harmonics have frequencies that are related to the fundamental frequency by simple multiples:

f1 = v/(2L)
f2 = 2 x f1
f3 = 3 x f1
f4 = 4 x f1

Resonance

Every system has a fundamental frequency, f1, that supports a standing wave.

f1, depends on the physical features of the system (length, density, temperature, etc).

Driving Force: A force that causes the oscillations.

When a driving force matches the fundamental frequency, the system will resonate.  The amplitude of the oscillation will increase to the limit of the system.

Example: The Tacoma Narrows Bridge.

Example: Earthquakes and buildings.

I also showed many other examples using my bowl, a spring, a metal bar, and the example of a kid on a swing.

More on Sound

 - Longitudinal wave in air, composed of compressions and rarefactions.

 - Wavelength is the distance between two compressions.

 - Frequency is directly related to pitch.

 - Amplitude is directly related to volume.

Humans can hear between 20 Hz and 20 000 Hz.

The speed of sound depends only on the medium (not on frequency or intensity).  You can only change the speed of sound by changing the air. ie. temperature.

In this equation, the speed of sound is in m/s and T is in degrees Celsius.

The speed of sound is referred to as Mach 1.

• Mach 2 is twice the speed of sound.
• Mach 3 is three times the speed of sound.
• etc...

Intensity

The intensity of sound (volume) is measured in Watts per meter squared.

  W / m^2

If area increases, intensity decreases.

Intensity is not often used because we can hear an incredibly large range of sound from  10^-12 W/m^2 up to 10 W/m^2.  That's a difference from 0.000000000001 W/m^2 up to 10 W/m^2!

We use a different scale to measure sound intensity called decibels.

Sound Intensity Level (dB)

More on this tomorrow....

Homework

Try the questions on the back of today's handout.