(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