C.2 Wave model

Solution outline

1. $\text{In a transverse wave, particles oscillate perpendicular to the direction of wave travel, producing crests and troughs.}$
2. $\text{Example: waves on a stretched string or certain surface water waves.}$
3. $\text{In a longitudinal wave, particles oscillate parallel to the direction of travel, forming compressions and rarefactions.}$
4. $\text{Example: sound waves in air.}$

Solution outline

1. $v = f\lambda.$
2. $v = 2.5\times0.80 = 2.0\ \mathrm{m\,s^{-1}}.$
3. $\text{The wave travels 2.0 m each second while each point on the surface oscillates 2.5 times per second.}$

Solution outline

1. $v = f\lambda \Rightarrow f = v/\lambda = 340/0.68 = 500\ \text{Hz}.$
2. $T = 1/f = 1/500 = 2.0\times10^{-3}\ \text{s}.$
3. $\text{A frequency of 500 Hz lies well within the typical human hearing range (about 20 Hz to 20 kHz).}$

Solution outline

1. $\text{EM waves are transverse disturbances in electric and magnetic fields, with the fields oscillating perpendicular to the direction of propagation.}$
2. $\text{They do not require a material medium and can travel through vacuum at speed } c \approx 3.0\times10^{8}\ \mathrm{m\,s^{-1}}.$
3. $\text{Sound waves are mechanical, longitudinal waves that require a material medium and travel much more slowly (about 340 } \mathrm{m\,s^{-1}} \text{ in air).}$

Solution outline

1. $\text{Mechanical waves require a material medium and involve oscillations of matter; EM waves can travel in vacuum and involve oscillating fields.}[web:180][web:290]$
2. \text{Mechanical waves can be transverse or longitudinal and typically have speeds that depend strongly on the medium; EM waves in vacuum all travel at speed } c.}[web:180][web:282]
3. $\text{Examples of mechanical waves: sound waves, waves on strings, water waves. Examples of EM waves: radio, microwaves, light, X‑rays.}[web:281][web:286]$

Solution outline

1. $\text{The graph shows compressions and rarefactions along the direction of travel, which is characteristic of a longitudinal wave.}[web:281][web:286]$
2. $\text{In a transverse wave graph, peaks and troughs represent displacements perpendicular to the direction of propagation instead.}[web:9][web:283]$