Question

The total energy of sound waves E is related to their frequency n as
(A) $E \propto n$
(B) $E \propto \dfrac{1}{n}$
(C) $E \propto \dfrac{1}{n^{2}}$
(D) $E \propto \dfrac{1}{\log n}$

Answer 1

Hint We know that sound is a mechanical wave and as such consists physically in oscillatory elastic compression and in oscillatory displacement of a fluid. Therefore, the medium acts as storage for both potential and kinetic energy. The frequency of sound waves is measured in hertz (Hz), or the number of waves that pass a fixed point in a second. Human beings can normally hear sounds with a frequency between about 20 Hz and 20,000 Hz. Sounds with frequencies below 20 hertz are called infrasound. There are two main properties of a regular vibration - the amplitude and the frequency - which affect the way it sounds. Amplitude is the size of the vibration, and this determines how loud the sound is. Frequency is the speed of the vibration, and this determines the pitch of the sound.

Complete step by step answer
We know that sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. The motion of the particles is parallel (and anti-parallel) to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves. Sound has two basic forms: acoustic energy and mechanical energy. Each type of sound has to be tackled in their own way. Acoustic energy or sound is what we experience every day. It is in fact vibration of air (sound waves) which is transformed by the tympanic membrane in the ear of humans to audible sounds.
However, sound waves are longitudinal waves and the particle motion associated with a standing sound wave in a pipe is directed along the length of the pipe (back and forth along the pipe axis, or left and right horizontally for the images shown at right). The vibrating drum skin causes nearby air particles to vibrate, which in turn causes other nearby air particles to vibrate. These vibrating particles make up a sound wave. When electricity is passed through a speaker, the diaphragm vibrates and produces sound waves, just like a drum.
The energy of a wave is related to its frequency using the formula, where f is the frequency of the wave.

Hence the correct option is option A.

Note We can say that sound cannot travel through a vacuum. A vacuum is an area without any air, like space. So, sound cannot travel through space because there is no matter for the vibrations to work in. Sound travels more quickly through solids than through liquids and gases because the molecules of a solid are closer together and, therefore, can transmit the vibrations (energy) faster. Sound travels most slowly through gases because the molecules of a gas are farthest apart. Sound travels faster in water compared with air because water particles are packed in more densely. Thus, the energy the sound waves carry is transported faster. The speed of sound is faster in solid materials and slower in liquids or gases. The velocity of a sound wave is affected by two properties of matter: the elastic properties and density.