In the limit as a pulse width (τ) for a given frequency (υ) goes to infinity, the frequency spread generated by the fft of the waveform goes to what? explain. if one wants to deliver radiation with a given frequency of very high precision to a sample, does the pulse need to be ‘short’ or ‘long’ ? explain. consider two arbitrary waveforms: one waveform is very sinusoidal in nature, the other is very “step-ish” and had non-smooth appearance. what can be said about the relative spread or distribution of sin/cos functions needed to reconstruct these waveforms?

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

Discuss how the hardness or softness of the landing surface is related to the time required to stop the egg

Which additional product balances the reaction h2so4 + 2naoh → na2so4 + 2h2o 2oh h2o2 h3o