Question

1.what is the frequency of the wave described by y = 5.6 sin(6.6x - 3πt), where distances are in mm, time in s?

2.Red light has an index of refraction in water of 1.331. What is the angle of incidence if the refracted angle in water is 32.0-degrees? (write out units)

3.What is the fundamental frequency for an open-open pipe that has a fourth harmonic of wavelength λ = 12.0 cm?

Note: Your answer is assumed to be reduced to the highest power possible.

Answer 1

(1)

The wave is given by

  

And so, the angular frequency of the wave is

  

And so, the frequency of the wave is

(2)

According to the Snell’s law, if the light ray is incident from medium 1 and is refracted in medium 2, then, the following equation is satisfied between the angle of incidence and the refracted angle:

So, if the incident medium (medium 1) is air and the refracted medium (medium 2) is water, then, putting the given values,

we calculate the incident angle as

This is the angle of incidence.

(3)

For an open-open tube, the frequency formula for the n the harmonic is given by

where, n = integer (1,2,3.....), and v is the speed of the sound and L is the length of the tube. And, the wavelength of the n the harmonic is

The fundamental frequency is for n = 1, i.e.,

So, replacing the length L in terms of the wavelength of the n th harmonic, we get

so, if the wavelength of the n=4 is given, then, by putting the given values,

We get the frequency of the fundamental mode