Physics of Music

Physics 341

Assignment 3

1) In the graph of dB versus frequency,

i) What frequencies correspond to -30dB? What pitches correspond to these frequencies?

Figure 1: Figure 1

ii)What dB correspond to 1500 Hz? 200Hz? 7000Hz?

Note: This curve is the "resonance response curve" of an oscillator whose resonant frequency is 440Hz. Ie, it is a plot of the energy in the oscillator if it is driven by the same amplitude of force at various frequencies. Note that far from the resonance the response falls at 6dB per octave in both directions. This is typical of all resonances.

2) In graph 2, Add the two waves to get the composite wave.

Figure 2

3) In graph 3, estimate which what the highest harmonic which would be neededto make up the complex wave form?

Figure 3

4)In graph 4 of the "spectrum" ( the Fourier components of a sound), which harmonics of the fundamental are present?

Figure 4

5) Sound travels at 340 m/sec in air at room temperature. What would be the wavelengths of sounds of i) 26Hz ii)110Hz iii)1760 Hz iv) 10 KHz ?

6) How much louder (in dB) is a choir of 80 voices than i)a single singer? ii) two singers iii) 10 singers. Assume that each singer produces the same energy output in sound while singing. How much closer (outdoors) would you have to be to the 10 voices so that they would be as loud as the 80 voices?

7)A string is plucked at a point 3/5 of the way from one end. Estimate the strength of vibration of the first 5 harmonics of the string. How would this compare to plucking the string at a distance 1/2 of the way from an end?