Transverse and Longitudinal Waves Elliott

Starter Write down two similarities and two differences between transverse and longitudinal waves.  Give one example of a transverse wave and one example of a longitudinal wave.

Answer Similarities – Both carry energy from one point to another; Both have a wavelength. Difference – The movement in a transverse wave is at 90o to the motion while in the longitudinal, the displacement is parallel;  There are regions of compression and rarefaction in a longitudinal wave. Example of a transverse wave: light waves.   Longitudinal wave: Sound wave .

Assumption We will assume that all waves are sinusoidal A sinusoidal wave-form (sine wave) is the simplest kind of wave.

E.M. Spectrum

The energy in the wave is inversely proportional to the wavelength: E - energy (J) h - Planck's Constant = 6.63 × 10-34 J s; c - speed of light = 3.0 × 108 m s-1; l - wavelength (m). 

Check Your Progress For a wave of wavelength 95 nm, calculate: (a) The frequency; (b) The photon energy in J and eV

Answer a. f = c/λ = 3.0 × 108 m s-1 ÷ 95 × 10-9 m = 3.2 × 1015 Hz   b. E = hc/λ = (6.63 × 10-34 J s × 3.0 × 108 m s-1) ÷ 95 × 10-9 m = 2.093 × 10-18 J = 2.1 × 10-18 J (2 s.f.)     E = 2.093 × 10-18 J ÷ 1.6 × 10-19 J eV-1 = 13.1 eV

Visible Light Visible light is a very small part of the electromagnetic spectrum. We can see wavelength from about 300 nm to 600 nm. Below 300 nm we have ultra-violet.    No animals can see infra-red, which has a wavelength longer than 700 nm, and this allows biologists to observe animals at night without disturbing them.

Activity Copy and complete the diagram with the primary and secondary colours of light. Label them.

Colour Addition If the light rays are super-imposed on each other, we get: Red + blue = magenta; Red + green = yellow; Green + blue = cyan; Red + green + blue = white. This process is called colour addition.

Check Your Progress Calculate: (a)    the frequency of the vibration of the speaker cones. (b)   the phase difference between the speaker signals. (c)    What kind of wave is being produced in the air by each speaker? (d)   Which speaker produces the loudest sound?  Explain your answer. (e)    The speed of sound in air is 340 m s-1.  What is the wavelength of the sound waves?

Answer (a) Period = 6 ms = 6 ´ 10-3 s Frequency = 167 Hz   (b) Phase difference = π radians because the crest of wave A meets a trough of wave B. (c) A longitudinal wave   because the speaker is compressing air molecules. (d) Loudspeaker A because the amplitude is 2 mm (while B is 1 mm). (e) λ= c/f = 340 m s-1 / 167 Hz = 2.04 m.