Explanation

(a) Conditions necessary for:
Constructive interference of waves

i. lt must involve at least two waves.

ii. Waves must vibrate in phase.

iii. The distance between the sources of the wave must be of the order of the wavelength.

Total internal reflection

i. The waves must travel from a denser medium to a less dense medium.

ii. The angle of incidence (in the denser medium) must be greater than the critical angle.

iii. It must involve two media of different optical densities.

Production of beats

1. The amplitude of the two interfering waves should be the same.

ii. The difference between the frequencies of interfering waves should be small.

iii. The two sources of waves must be sounded together.

(b) Calculation of velocity of sound in air

V = f\(\lambda\)

V = 2f(l\(_{2}\) - l\(_{1}\))

= 2 x 256(100 - 35)

= 33280 cm s\(^{-1}\)

= 332.80 m s\(^{-1}\)

(c)(i) Classification of musical instruments

i. Wind

ii. Stringed

iii. Percussion

(ii) Examples of classified instruments saxophone

I. Wind: flute, trumpet, pipe, organ,

iii. Stringed: piano, guitar, violin

iii. Percussion: piano, drum, bell, gong. xylophone

(d) Calculation of critical angle

\(\eta\) = \(\frac{1}{\text {Sin C}}\)

1.5 = \(\frac{1}{\text {Sin C}}\)

Sin C = 0.667

C = 41.80º

(e) Calculation of temperature

\(\frac{V_{1}}{\sqrt T_{1}} = \frac{V_{2}}{\sqrt T_{2}}\)

\(\frac{240} {\sqrt 375} = \frac {310} {\sqrt T_{2}}\)

240 \(\sqrt T_{2}\) = 310 x 19.36

\(\sqrt T_{2}\) = 625 K = 352 ºC

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