• If two sounds are only slightly off in terms of frequency The ‘Beats’

Produce a periodic rise and fall of amplitude (volume)

Throbbing Sound = Beats

• #‘beats’ = how far apart the two frequencies are

The ‘Beats’

Ex. Tuning Fork 1: f = 440 HzTuning Fork 2: f = *Beat Frequency of 2 Hz?

• A guitar string produces 4 beats per second when tuned with a 350 Hz tuning fork and 9 beats per second when tuned with a 355 Hz tuning fork. What is the actual frequency of the guitar?

Example 8

• What about the rubber bands determines pitch?Musical Instruments - Strings

The pitch or frequency of a string is determined by the string’s velocity (how fast it can move back and forth)

FT = Force of Tensionm/L = (mass)/(Length) = Linear Density

Tension Thickness

• When the tension in a particular cord is 75.0 N, the wave velocity is 130.0 m/s. If the length of the cord itself is approximately 26.0 inches (1 in = 25.4 mm), what is the mass of the cord?

Example 9

• Standing Wave – aka Stationary Waves – waves that appear still. Created by overlapping waves.

Standing Waves

Two Parts of a Standing Wave Nodes: No movement

Anti-Nodes: Maximum vibration

• Sound (musical notes) will have some sort of repeating pattern

Difference Between Notes and Noise

• Tuning Forks – Produce one frequency (pure tone)

Standing Waves w/ Musical Instruments

When a note is played, the primary sound = Fundamental frequency

Within each fundamental frequency are other frequencies – The harmonics

Musical instruments sound different from tuning forks – due to their timbre (tone quality or tone color)

Difference in timbre – due to the instruments harmonics

Standing Waves - Strings Different frequencies are produced by different harmonics

Fundamental First Harmonic (f1)

Number of Loops = 1

Second Harmonic (f2) Number of Loops = 2 f2 =2(f1) Third Harmonic (f3) Number of Loops = 3 f3 =3(f1) Fourth Harmonic (f4) Number of Loops = 4 f4 =4(f1)

• Frequencies for standing waves:Standing Waves - Strings

n = number of the harmonicL = Length of the vibrating stringv = velocity of a

string*Different notes are achieved by changing the

length of the vibrating string.

• A particular string on a piano is 1.50 m long and has a tension of 400.0 N. It vibrates with a fourth-harmonic frequency of 110.0 Hz.

A. What is the mass of this string? B. What are the first three harmonics of this string?

Example 10