(a) On which day would sound wave travel faster: on a hot or cold day? Explain.
(b) Why are megaphones shaped like funnels?
(c) A ray of light is incident on a surface of a ectangular glass prism of refractive index 1.5 illustrated in the diagram below.
(i) Copy the diagram a label the angles of: ((alpha)) Incidence (x); ((beta)) Reflection (y); ((gamma)) refraction (z); with t glass letters indicated.
(ii) Calculate the angle refraction to the nearest whole number.
(d) A sonomesr wire vibrates in simple harmoi motion with a maximum amplitude of 1.0 cm. Calculate the frequency of vibration of the wire, giv that the magnitade of the maximum acceleration of the wire is 980ms(^{-2}). [(pi frac{22}{7})]
Explanation
(a) Sound wave travels faster on a hot day because the speed of sound is proportional to the square root of absolute temperature (V (alpha sqrt{T})), hence the higher the greater the speed of sound wave.
(b) Megap:iones are shaped like a funnels because at the smaller end of the cone, the sound energy comes into contact will a small mass of air producing greater intensity. As it comes out of the larger open end, the energy sets a larger air mass into vibration, hence the final sound is louder.
(c) (i)
(ii) n = (frac{sini}{sinr})
sinr = (frac{sini}{n} = frac{sin60}{1.5})
= (frac{0.8660}{1.5} = 0.5774)
r = sin(^{-1})0.5774 = 35(^{o})
(d) a = (Omega^2r) but (Omega = 2 pi f)
a = (2(pi f)^2)r
f = (sqrt{frac{9}{4 pi^2 r}} = sqrt{frac{988}{4(frac{22}{7})^2} times frac{1}{100}})
= 50Hz