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x(t) above since the frequencies are too low However, we can make a similar combination with signals at frequencies humans can hear For example, consider the signal d(t) = sin(2 £350£t)+sin(2 £440£t) Each of the two sinusoids (at frequencies 350 Hz and 440 Hz) alone corresponds to a pure tone that can be heard by the normal human ear
Hz third harmonic, 250 Hz fifth harmonic and the 350 Hz seventh harmonic Generally, single-phase loads generate the third harmonic and three-phase loads generate the other harmonics The fifth and the seventh harmonics can be filtered out by so called “tuned circuits” Until recently, there was no economic way to filter the third harmonic
The 880 Hz and 1320 Hz frequencies are called _____ in this example a) fundamentals b) harmonics c) tertiary frequencies d) formants 3 Frequency can be coded by the firing rate at or near the peak of a 200 Hz sine-wave pressure change (sound) This is called a) frequency coding b) place theory c) phase locking d) a & c above 4
Sine-on-Random Example: Use the same background random as defined above, and add in sine tones of 1 0G peak at 50 Hz, 2 0 G peak at 80 Hz, and 1 5 G peak at 110 Hz Frequency Acceleration Acceleration Squared (Hz) G Peak G RMS G2 random - 6 064 36 77 50 1 0 0 707 0 50 80 2 0 1 414 2 00 110 1 5 1 061 1 13 Total 40 40
1 The musical note A above middle has a frequency of 440 Hz If the speed of sound is known to be 350 m/s, what is the wavelength of this note? ` Practice Problem: Wave Speed f = 440 Hz v = 350m/s = ? = v/f = 350 m/s 440 Hz = 0 80 m 2 A certain FM radio station broadcasts electromagnetic waves at a frequency of 9 05 x 107 Hz These radio waves
2 What frequency is heard when a car approaching you at 25 m/s honks his horn with a frequency of 350 Hz? a) 320 Hz b) 380 Hz c) 420 Hz d) 460 Hz e) Either a or b 3 A simple harmonic oscillator moves according to the equation x = 0 25 cos 2 2t If the maximum velocity is 2 8 m/s what will the velocity be when x = 0 14 m?
The equation above is not an equation for a traveling wave (it actually is very similar to a harmonic oscillator) This type of equation is for a standing wave Every element of the medium vibrates with the same frequency, but the amplitude of oscillation depends on the position is space The points of maximum amplitude are called