WAEC Physics 2022 Theory — Question 11

Model answer

(a)(i) Conditions for constructive interference of waves: It must involve at least two waves; waves must vibrate in phase; the distance between the sources of the wave must be of the order of the wavelength. (ii) Conditions for total internal reflection: The waves must travel from a denser medium to a less dense medium; the angle of incidence (in the denser medium) must be greater than the critical angle. (iii) Conditions for production of beats: The amplitude of the two interfering waves should be the same; the difference between the frequencies of interfering waves should be small; the two sources of waves must be sounded together. (b) Calculation of velocity of sound in air: l₁=35cm, l₂=100cm are lengths of air column for two consecutive resonance positions when tuning fork of frequency f is sounded. l₂−l₁=λ/2, so λ=2(l₂−l₁)=2(100−35)−(end correction adjustments)=2×65=130cm (approx, per standard resonance tube method, adjusting for end correction) v=fλ=2×256×(100−0.35)=... per source's detailed calculation, v=332.80m/s. (c)(i) Three classifications of musical instruments: Wind; Stringed; Percussion. (ii) Examples: wind — flute, trumpet, pipe, organ; stringed — piano, guitar, violin; percussion — drum, bell, gong, xylophone. (d) Calculation of critical angle: n=1/sinC. 1.5=1/sinC. sinC=0.6667. C=sin⁻¹0.6667=41.80°. (e) Using v∝√T (speed of sound proportional to square root of absolute temperature): V₁/√T₁=V₂/√T₂. T₁=102+273=375K, V₁=240m/s, V₂=310m/s. √T₂=(310×√375)/240=25.0067. T₂=625.3K.