(a) State one condition each necessary for the characteristics each of the following occurrences:
(i) Constructive interference of waves.
(ii) Total internal reflection.
(iii) Production of beats.
(ii) Give one example each of the classifications stated in (c)(i).
(d) Calculate the critical angle for light traveling from glass to air. [refractive index of glass = 1.5].
(e) The speed of sound in a medium at a temperature of 102 °C is \(240\ \mathrm{m\ s}^{-1}\). If the speed of sound in the medium is \(3\ 10\ \mathrm{m\ s}^{-1}\). Calculate its temperature
(a)
(i) One necessary condition for constructive interference of waves is that the waves have the same frequency, and the crests and troughs of the waves align with each other.
(ii) One necessary condition for total internal reflection is that the angle of incidence is greater than the critical angle for the boundary between two media, and the wave travels from a denser medium to a less dense medium.
(iii) One necessary condition for the production of beats is that two waves with slightly different frequencies interfere with each other, and their amplitudes vary periodically in time.
(b) The velocity of sound in air can be calculated as follows:
- The distance between the first and second position of resonance is 100 cm - 35 cm = 65 cm = 0.65 m.
- The wavelength of the sound wave is twice the distance between the first and second position of resonance, which is 2 x 0.65 m = 1.3 m.
- The frequency of the tuning fork is 256 Hz. - Using the equation v = fλ, where v is the velocity of sound, f is the frequency, and λ is the wavelength, we can calculate the velocity of sound as
v = 256 Hz x 1.3 m = 332.8 m/s.
(c) (i) The three classifications of musical instruments are:
- Stringed instruments
- Wind instruments
- Percussion instruments
(ii) Examples of each classification are:
- Stringed instruments: guitar, violin
- Wind instruments: flute, trumpet
- Percussion instruments: drums, xylophone
(d) The critical angle for light traveling from glass to air can be calculated as follows:
- The refractive index of glass is given as 1.5.
- Using the formula sin ?c = 1/n, where ?c is the critical angle and n is the refractive index, we can calculate the critical angle as sin θc = 1/1.5 = 0.67.
- Taking the inverse sine of 0.67, we can find the critical angle as θc = 42.3 degrees.
(e) The speed of sound in a medium is directly proportional to the square root of the temperature of the medium. Using this relationship, we can calculate the temperature of the medium as follows:
- Let T1 be the temperature of the medium where the speed of sound is 240 m/s, and T2 be the temperature of the medium where the speed of sound is 310 m/s.
- The ratio of the speeds of sound is 310/240 = 1.29.
- The ratio of the square roots of the temperatures is √(T2/T1) = 1.29. - Solving for T2, we get T2 = T1 x (1.29)^2 = T1 x 1.6641. - Substituting T1 = 102 + 273 = 375 K, we get T2 = 625 K. -
Therefore, the temperature of the medium where the speed of sound is 310 m/s is 625 - 273 = 352 °C.
