Answer
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Hint: Wavefront describes the movement of sound from the source and has its origin in Hygen’s principle. According to it, Sound moves equally in all directions and there cannot be a backward flow of energy and hence no backward wavefront. We can make use of formula for speed to find out the answer of part (a)
Complete Step by step solution:
(a) using the relationship between speed, distance and time we get.
\[\Delta t=\dfrac{d}{v}=\dfrac{D\sin \theta }{v}\]
(b) since, the speed of the sound in water is now \[{{v}_{n}}\] with \[\theta ={{90}^{0}}\], we have
\[\Delta {{t}_{w}}=\dfrac{D\sin \theta }{{{v}_{w}}}=\dfrac{d}{{{v}_{w}}}\]
(c) now to find the apparent angle we can do that as, \[\Delta t=\dfrac{D\sin \theta }{v}=\dfrac{d}{{{v}_{w}}}\]
Solving for the angle \[\theta \]with \[{{v}_{w}}=1482m/s\] we get,
$\Rightarrow \theta ={{\sin }^{-1}}(\dfrac{v}{{{v}_{w}}}) \\
\Rightarrow \theta ={{\sin }^{-1}}(\dfrac{343}{1482}) \\$
$343m/s$ being the speed of sound in air,
$\Rightarrow {{\sin }^{-1}}(0.231) \\
\therefore {{13}^{0}} \\$
Note: Trigonometric ratios are unitless but angles can be measured either in degrees or radians. All the units to be taken in standard SI units of system. A wavefront is a surface over which a wave has a constant phase. Wavefront came into existence from Hygen’s theory of wave picture of light. Wavefront determines the nature and propagation of a light emanating from the given source.
One should always keep in mind that frequency is the characteristic of the source of the light
Complete Step by step solution:
(a) using the relationship between speed, distance and time we get.
\[\Delta t=\dfrac{d}{v}=\dfrac{D\sin \theta }{v}\]
(b) since, the speed of the sound in water is now \[{{v}_{n}}\] with \[\theta ={{90}^{0}}\], we have
\[\Delta {{t}_{w}}=\dfrac{D\sin \theta }{{{v}_{w}}}=\dfrac{d}{{{v}_{w}}}\]
(c) now to find the apparent angle we can do that as, \[\Delta t=\dfrac{D\sin \theta }{v}=\dfrac{d}{{{v}_{w}}}\]
Solving for the angle \[\theta \]with \[{{v}_{w}}=1482m/s\] we get,
$\Rightarrow \theta ={{\sin }^{-1}}(\dfrac{v}{{{v}_{w}}}) \\
\Rightarrow \theta ={{\sin }^{-1}}(\dfrac{343}{1482}) \\$
$343m/s$ being the speed of sound in air,
$\Rightarrow {{\sin }^{-1}}(0.231) \\
\therefore {{13}^{0}} \\$
Note: Trigonometric ratios are unitless but angles can be measured either in degrees or radians. All the units to be taken in standard SI units of system. A wavefront is a surface over which a wave has a constant phase. Wavefront came into existence from Hygen’s theory of wave picture of light. Wavefront determines the nature and propagation of a light emanating from the given source.
One should always keep in mind that frequency is the characteristic of the source of the light
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