State what is meant by the frequency of a progressive wave.
A cathode-ray oscilloscope (c.r.o.) is used to find the frequency of the sound produced by a loudspeaker. The trace on the c.r.o. screen is shown in Fig. 4.1. The time-base setting of the c.r.o. is $250\,\mu\text{s}\,\text{cm}^{-1}$. Show that the frequency of the sound wave is $1600\,\text{Hz}$.
The loudspeaker in (b) sends sound out in every direction. A person fastens the loudspeaker to a string and then whirls it in a horizontal circle above his head at constant speed. An observer, a long distance from the loudspeaker, hears sound with maximum frequency $1640\,\text{Hz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. Determine the speed of the loudspeaker.
Describe and explain, qualitatively, how the frequency of the sound heard by the observer changes.