Harmonics problem. A square wave of frequency f contains harmonics (sine waves) at f, 3f, 5f, 7f, ... . Suppose a system responds to frequencies in the range 20-40 kHz but is insensitive outside of this range. EXAMPLE:Imagine applying a square wave with f = 30 kHz to this system. What is the shape of the response?[ a 30 kHz sine wave. ]Imagine applying a square wave with f = 10 kHz to this system. What is the shape of the response?A. A 10 kHz sine waveB. A combination of 20, 30 and 40 kHz sine wavesC. A 30 kHz sine waveD. No response

B

Explanation:

A square of frequency of consists of the infinite sum of sine waves, whose frequencies are the odd multiples of the main frequency f i.e f, 3f,5f, 7f, ... . Given that the range of frequencies, to which the system responds is 20-40 kHz, for a square wave of frequency 10kHz we need to look for the harmonics whose frequencies are in the systems' respond range, which are the  harmonics of 20, 30 and 40 kHz

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide

you get 2.3=1.21*\frac{a}2 or 4.6=1.21a or a=3.802 (b)

explanation: