Physics

Physics

Problem

A loudspeaker cone completes one vibration in 0.004 s0.004\,\text{s} and sends sound into still air where the speed of sound is 340 m/s340\,\text{m/s}. a. (i) Determine the frequency and the time period of the sound produced. b. (ii) Calculate the wavelength of this sound in air. c. (iii) The amplitude of vibration of the cone is now doubled while the frequency is kept the same. State and explain the effect, if any, on (a) loudness, (b) wavelength, and (c) speed of sound. d. (iv) Later, the air temperature rises and the speed of sound becomes 350 m/s350\,\text{m/s}. Determine the new wavelength, assuming the frequency remains unchanged.
Intuitive explanation

The key is connecting the cone's vibration rate to the wavelength of the sound it produces. Since the cone completes one full cycle in 0.004 s0.004\,\text{s}, you can find its frequency—how many vibrations happen per second. Then use the wave relationship v=fλv = f\lambda to find the wavelength: the frequency tells you how tightly the sound waves are packed, and the speed of sound tells you how fast they travel through air.

Intuitive explanation

The key is connecting the cone's vibration rate to the wavelength of the sound it produces. Since the cone completes one full cycle in 0.004 s0.004\,\text{s}, you can find its frequency—how many vibrations happen per second. Then use the wave relationship v=fλv = f\lambda to find the wavelength: the frequency tells you how tightly the sound waves are packed, and the speed of sound tells you how fast they travel through air.

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