Respuesta :
Answer:
(a). The angle of refraction for the sound wave is 61.8°.
(b). The wavelength of the sound in water is 2.56 m.
(c). The angle of refraction is 8.26°.
(d). The wavelength of the light in water is 441.75 nm.
Explanation:
Given that,
Wavelength = 589 mm
Incidence angle = 11.7°
We know that,
The speed of sound in water is GREATER than the speed of sound in air by a factor of about 4.3 times.
The speed of sound wave in water
[tex]v_{w}= 1493\ m/s[/tex]
The speed of sound wave in air at 20°C
[tex]v_{a}= 343\ m/s[/tex]
(a). We need to calculate the angle of refraction for the sound wave
Using Snell's law
[tex]\dfrac{\sin\theta_{1}}{v_{a}}=\dfrac{\sin\theta_{2}}{v_{w}}[/tex]
Put the value into the formula
[tex]\dfrac{\sin11.7}{343}=\dfrac{\sin\theta_{2}}{1493}[/tex]
[tex]\sin\theta_{2}=\dfrac{\sin11.7}{343}\times1493[/tex]
[tex]\sin\theta_{2}=0.882[/tex]
[tex]\theta_{2}=\sin^{-1}(0.882)[/tex]
[tex]\theta_{2}=61.8^{\circ}[/tex]
The angle of refraction for the sound wave is 61.8°.
(b). We need to calculate the wavelength of the sound in water
Using formula of wavelength
[tex]\dfrac{v_{w}}{\lambda_{w}}=\dfrac{v_{a}}{\lambda_{a}}[/tex]
Put the value into the formula
[tex]\dfrac{1493}{\lambda_{w}}=\dfrac{343}{0.589}[/tex]
[tex]\lambda_{w}=\dfrac{1493\times0.589}{343}[/tex]
[tex]\lambda_{w}=2.56\ m[/tex]
The wavelength of the sound in water is 2.56 m.
(c). We need to calculate the angle of refraction
Using formula of Snell's law
[tex]n=\dfrac{\sin\theta_{i}}{\sin\theta_{r}}[/tex]
[tex]\dfrac{4}{3}=\dfrac{\sin11.7}{\sin\theta_{r}}[/tex]
[tex]\sin\theta_{r}=\dfrac{\sin11.7\times3}{4}[/tex]
[tex]\theta_{r}=\sin^{-1}(0.1437)[/tex]
[tex]\theta_{r}=8.26^{\circ}[/tex]
The angle of refraction is 8.26°.
(d). We need to calculate the wavelength of the light in water
Using formula of wavelength
[tex]\lambda_{w}=\dfrac{\lambda_{a}}{n}[/tex]
Put the value into the formula
[tex]\lambda_{w}=\dfrac{589}{\dfrac{4}{3}}[/tex]
[tex]\lambda_{w}=441.75\ nm[/tex]
The wavelength of the light in water is 441.75 nm.
Hence, This is the required solution.
