The velocity of sound in air is about 330m/s, and in water is about 1700m/s. Calculate the critical angle for sound leaving air and entering water.
sinTheta*1=sin90*(330/1700)
theta= arcsin( )=11.19 degrees
That speed is a bit high for water. https://hypertextbook.com/facts/2000/NickyDu.shtml
To calculate the critical angle for sound leaving air and entering water, we can use Snell's law. Snell's law relates the angles and velocities of waves as they pass between different media.
The equation for Snell's law is:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the refractive index of the medium the wave is leaving (air in this case),
- theta1 is the angle of incidence (the angle the wave makes with the normal to the interface),
- n2 is the refractive index of the medium the wave is entering (water in this case),
- theta2 is the angle of refraction (the angle the wave makes with the normal to the interface).
In this case, the velocity of sound in air is 330 m/s, and the velocity of sound in water is 1700 m/s. The refractive index (n) of a medium is given by the ratio of the velocity of sound in a vacuum (v0) to the velocity of sound in the medium (v), so we have:
n1 = v0 / v1
n2 = v0 / v2
Using the given velocities, we can calculate the refractive indices:
n1 = 330 m/s / 330 m/s = 1
n2 = 330 m/s / 1700 m/s ≈ 0.194
Now, let's rearrange Snell's law to solve for theta2:
sin(theta2) = (n1 / n2) * sin(theta1)
Since we're interested in the critical angle, which is the angle of incidence when the angle of refraction is 90 degrees, we can set theta2 equal to 90 degrees and solve for theta1:
sin(90 degrees) = (n1 / n2) * sin(theta1)
sin(theta1) = (n2 / n1) * sin(90 degrees)
sin(theta1) = (0.194 / 1) * 1
sin(theta1) = 0.194
To find the critical angle, we need to find the inverse sine (or arcsin) of sin(theta1):
theta1 = arcsin(0.194)
Using a scientific calculator or trigonometric table, we find that arcsin(0.194) ≈ 11.27 degrees.
Therefore, the critical angle for sound leaving air and entering water is approximately 11.27 degrees.