A. When we are designing the sound levels to ensure a clear reception by a human ear, we often express the sound intensity in a unit called dB. The intensity level in dB of a sound wave can be found...

Extracted text: A. When we are designing the sound levels to ensure a clear reception by a human ear, we often express the sound intensity in a unit called dB. The intensity level in dB of a sound wave can be found by converting the sound intensity produced by the speakers, I, expressed in Watts/m², using the formula: B(dB) = 10log10G) Where: B is the sound intensity level in dB. I is the sound wave intensity in W/m². I, is a constant representing the intensity threshold of hearing, which is the lowest intensity a human can hear with his/her ears. A sound source, or a speaker, produces a wave with intensity I, which varies with respect to time as given below: 1 = 3+2 cos(4t – ) W/m². Knowing that I, = 1 x 10-1" W/m²: 1. Find a formmila for the rate of change of B with respect to time. [Hint: use the chain rule] 2. Find the value of the rate of change of B with respect to time at t = 1 sec. B. The speed [v] of the sound wave travelling across the stadium is found to have the following equation: Where: 0 < 3.5="" x="" is="" the="" distance="" travelled="" across="" the="" stadium="" in="" 100="" meter="" units="" [="" x="1," means="" a="" distance="" of="" 100="" meters,="" x="2" a="" distance="" of="" 200="" meters,="" and="" so="" on],="" evaluate:="" 1.="" the="" stationary="" points="" of="" the="" velocity="" function="" for="" the="" range=""><>< 3.5.="" 2.="" define="" which="" stationary="" point="" represents="" a="" maximum="" velocity,="" a="" minimum="" velocity,="" and="" an="" inflexion="" point="" in="" the="" velocity="" within="" the="" specified="" period.="" use="" higher="" order="" derivatives="" test="" for="" finding="" these="" points="" and="" show="" your="" solution="" step-by-step.="" 3.="" use="" excel="" or="" matlab="" to="" draw="" the="" function="" v="" and="" its="" first="" and="" second="" derivatives="" v'="" and="" v",="" for="" 0="">< x="">< 3.5. then use these curves to confim that the points you have found are minimum, maximum and inflexion points by stating the behaviour of each of the three curves at each of these points. 3.5.="" then="" use="" these="" curves="" to="" confim="" that="" the="" points="" you="" have="" found="" are="" minimum,="" maximum="" and="" inflexion="" points="" by="" stating="" the="" behaviour="" of="" each="" of="" the="" three="" curves="" at="" each="" of="" these="">