You can synthesize music (singals) several ways. One is the additive method where your sum pure sinusoids to build up a signal (Fourier expansion). Another method is the subtractive method where you create harmonics with square or saw-toothed wave and filter out the parts you do not want. Plot at least 7 non-zero terms of amplitude/phase line spectra of a saw-toothed wave form so that a sound engineer can evaluate which signals are available for manipulation

Ball b is hanging from an inextensible cord. an identical ball a is released from rest when it is just touching the cord and drops through the vertical distance h a 5 8 in. before striking ball b. assuming e 5 0.9 and no friction, determine the resulting maximum vertical displacement h b of the ball b

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

Natural forces that can alter ecosystems include seasons and climate changes. t or f