(a) If two sound waves, one in air and one in (fresh) water, are equal in intensity and angular frequency, what is the ratio of the pressure amplitude of the wave in water to that of the wave in air? Assume the water and the air are at . (See Table 14-1.)
(b) If the pressure amplitudes are equal instead, what is the ratio of the intensities of the waves?
We can use the equation of intensity of the wave in the relation between displacement amplitude and pressure amplitude to find the ratio of the pressure amplitude of the wave in water to that of the wave in the air if two sound waves are equal in intensity and angular frequency.
The intensity of the wave,
The displacement amplitude of the wave,
role="math" localid="1661508014075" …(ii)
The pressure amplitude of the wave,
Using equation (ii) in equation (iii), we get the pressure amplitude as:
So, the ratio of the pressure amplitudes of water to air using equation (a) is given as:
Therefore, the ratio of the pressure amplitude of the wave in water to that of the wave in air if two sound waves are equal in intensity and angular frequency is
From equation (a), we get the intensity of the wave as:
So, the ratio of the intensities of water to air using equation (b) is given as:
Therefore, the ratio of the intensities of the waves if the pressure amplitudes are equal is .
A point source that is stationary on an x-axis emits a sinusoidal sound wave at a frequency of and speed. The wave travels radially outward from the source, causing air molecules to oscillate radially inward and outward. Let us define a wavefront as a line that connects points where the air molecules have the maximum, radially outward displacement. At any given instant, the wavefronts are concentric circles that are centered on the source. (a) Along x, what is the adjacent wavefront separation? Next, the source moves along at a speed of. Along x, what are the wavefront separations (b) in front of and (c) behind the source?
A certain loudspeaker system emits sound isotropically with a frequency of and an intensity of role="math" localid="1661500478873" at a distance of role="math" localid="1661501289787" . Assume that there are no reflections. (a) What is the intensity at ? At , what are (b) the displacement amplitude and (c) the pressure amplitude?
When you “crack” a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The sudden production of the bubble, called “cavitation,” produces a sound pulse, the cracking sound. Assume that the sound is transmitted uniformly in all directions and that it fully passes from the knuckle interior to the outside. If the pulse has a sound level of at your ear, estimate the rate at which energy is produced by the cavitation?
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