Problem — True or false on waves and Doppler

Problem

True or false? (a) Sound waves are longitudinal waves. (b) Visible light is a longitudinal wave. (c) In a string fixed at both ends, only standing waves with specific frequencies can exist. (d) The Doppler effect applies to any type of wave. (e) The frequency of a wave changes when it passes from one medium to another.

Solution

(a) True. In sound, the particles of the medium oscillate along the direction of propagation: a longitudinal wave.

(b) False. Light (an electromagnetic wave) is transverse: the fields $\vec E$ and $\vec B$ oscillate perpendicular to the direction of propagation (which is why it can be polarised).

(c) True. The constraints at the ends (fixed nodes) select only the frequencies $f_n = n\,v/2L$: the harmonics. Other frequencies do not give stable standing waves.

(d) True. The Doppler effect is a general phenomenon of relative motion between source/observer and applies to sound, light and every type of wave.

(e) False. Passing from one medium to another, the frequency stays constant (it is set by the source); instead the speed $v$ changes, and so does the wavelength $\lambda = v/f$.

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Links

Topics: Onde Concepts: Effetto Doppler · Onda armonica