# Questions on Sounds

What are the frequencies of the first four harmonics of middle C (261.6Hz)? Approximately how many times louder is a 110 dB sound than a 80 dB sound?

a) $F1 = 261.6 Hz$, fundamental or so called first harmonic

Second harmonic harmonic frequency $F2 = 261.6*2 =522.4$ Hz

Third harmonic frequency $F3 =261.2*3 = 783.6$ Hz

Fourth harmonic freq. $F4 = 261.2*4 = 1044.8$ Hz

Fifth harmonic freq. $F5 =261.2*4 = 1306$ Hz

b) By definition the intensity I of a sound in decibels is given by the relation

$dB = 10*log(I/I0)$, where $I0$ is the reference intensity and $I0=10^{-12}$ W/m^2 and the log is taken in base 10.

Therefore

$110 =10*log (I1/I0)$

$80 =10*log(I2/I0)$

$10^{11} = I1/I0$

$10^8 =I2/I0$

and by dividing one has

$10^{(11-8)} = I1/I2$

$I1/I2 =100$

$I1 =100*I2$

Thus the 110 dB sound is 100 times louder than the 80 dB sound.