A damped sine can be created from the formula s(t) = e^at sin (2 pi ft), where f
ID: 3161241 • Letter: A
Question
A damped sine can be created from the formula s(t) = e^at sin (2 pi ft), where f is the frequency and alpha is a positive number called the damping constant. damping reduces the amplitude of s(t) as times t increase. If alpha is very small there is hardly any damping at all and if alpha is large the amplitude goes to zero very fast. The figure below shows the spectrograms of three damped sine waves. a) What are the frequencies of the 3 sinusoids? b) In the first 0.1 s, which one of sinusoids (1) and (3) has the lowest amplitude? why? c) Which one of sinusoids (2) and (3) has a lower value of the damping constant? why?Explanation / Answer
a) The mean frequencies are
1Hz for sinusoid 1 , 2Hz for sinusoid 2 and 3Hz for sinusoid 3
b)For the first 0.1s,
sinusoid 3 has a larger amplitude than sinusoid 1.
This is because sinusoid 3 is more intense than sinusoid 1.
c)Sinusoid 3 has a lower damping constant than sinusoid 2 because the intensity of sinusoid 2 fades out faster than sinusoid 3. This means amplitude of sinusoid 2 decreases faster than sinusoid 3.