The frequency of light does not change when it enters a medium with a different index of refraction; in this case, that new medium is the glass of the prism. From the velocity of light equation we know the relationship between velocity and frequency.

v is the velocity of light,  is the wavelength, and f is the frequency. When light enters the prism, its velocity changes due to the new index of refraction, but its frequency remains constant.

Because the frequency does not change, we can see that velocity is directly proportional to wavelength; thus, the shorter the wavelength, the slower the velocity. So both wavelength and velocity change when frequency is constant. 

The period of a wave is equal to the reciprocal of the frequency:

Respectively, frequency is the reciprocal of period. By definition, the product of two reciprocals is one.

Wave velocity is given by the product of frequency and wavelength:

In the question, we are given the period (waves per second). To find the frequency, we will need to take the reciprocal of the period.

Using the values given in the question, we can find the velocity of the waves. The wavelength is twice the distance between adjacent maxima and minima, making our wavelength two meters.

The relationship between wavelength and frequency is given by the equation:

In this case, the velocity will be equal to the speed of light.

Using this value and the given wavelength, we can find the frequency of the photon. Keep in mind that the wavelength must be given in meters.

Solve for frequency by taking the inverse of the period.

Next, solve for wavelength by dividing velocity by frequency.

The beat frequency is simply the difference between two frequencies.

We are given the frequency of each tuning fork, so we can use the equation to solve for the beat frequency.

Beat frequency is the difference between the two frequencies.

200Hz – 150Hz = 50Hz

Using the equation  we can find the frequency of the soundwave. 

Sound waves are longitudinal waves, meaning that the waves propagate by compression and rarefaction of their medium. They are termed longitudinal waves because the particles in the medium through which the wave travels (air molecules in our case) oscillate parallel to the direction of motion. Alternatively, transverse waves oscillate perpendicular to the direction of motion. Common examples of transverse waves include light and, to a basic approximation, waves on the ocean.

Longitudinal waves transmit energy by compressing and rarefacting the medium in the same direction as they are traveling. Sounds waves are longitudinal waves and travel by compressing the air through which they travel, causing vibration.

Light, X-rays, and microwaves are all examples of electromagnetic waves; even if you cannot recall if they are longitudinal or transverse, they are all members of the same phenomenon and will have the same type of wave transmission. Transverse waves are generated by oscillation within a plane perpendicular to the direction of motion. Oscillating a rope is a transverse wave, as it is not compressing in the direction of motion.