Physics- waves and optics

How do you get clear interference patterns from two or more separate sources of waves?

The sources must be in phase and of the same fixed wavelength and frequency

What is path difference, and what depends on it?

Path difference is how much further one wave has to travel than another to reach a certain point, and whether constructive or destructive interference occurs is dependent on it. If a point has nλ or 0 path difference where n ∈ Z then constructive interference occurs. If the path difference between two waves is nλ + 1/2λ then destructive interference will occur and no sound will be heard

How is a stationary wave formed?

When two progressive waves with equal frequency (wavelength) move in opposite directions to one another and superpose, a standing wave is formed

How does one create a standing wave with a string?

On one end, a driving oscillator is tied to a string, which is tightly tied to a fixed point on the other end. This means that the wave that the oscillator creates becomes reflected. If the oscillator produces a whole number of waves between the time it takes for a wave to travel to one end and back again, then a standing wave is formed as the original and reflected waves reinforce one another.

What are resonant frequencies?

Frequencies of a wave source (usually a vibrating oscillator) that creates a wave that travels from one end and back again in the same amount of time that the wave source produces a whole number of waves, thereby creating a standing wave where the patterns of nodes and antinodes do not move

What is a standing wave?

A wave where the pattern (of peaks and troughs) do not move

What happens at the resonant frequency of a standing wave in terms of wavelengths?

an exact number of half wavelengths fit on the standing wave

How do you set up and detect a standing wave using a microwave transmitter?

Place a microwave transmitter facing a metal plate and create a standing wave by reflecting the microwaves off of it. Move a microwave probe between the plate and transmitter and connect it to a meter. The points where the meter reads the largest are the nodes, and the points where there are no readings are the antinodes

How do you detect a standing wave using powder, a speaker and a glass tube

The speaker is inserted at one end of the glass tube with the other end being covered. The speaker should emit sound waves at such a frequency that when they are reflected, they form a standing wave. This standing wave will shake away the powder at the antinodes thereby pushing it towards the nodes, meaning the powder will gather at the nodes

How investigate the factors affecting resonant frequency on a string?

take multiple strings, and measure their masses and lengths, then calculate the mass per unit length of each string (μ) using μ=M/L.

Then, on a level bench , tie one end of a given string to a vibration transducer which is in turn wired to a signal generator, and tie the other end to a fixed number of masses, and hang the string with the masses attached over a pulley. Measure and record the length of the string between the end tied to the vibration transducer and the pulley using a meter rule, record the μ value of the string and calculate and record the tension (T) in the string using T=Mg

Turn on the signal generator and change the frequency until you reach the frequency of the first harmonic (f), a wave which has two nodes at either and an antinode in the middle. Record this

To see how length affects resonant frequency, keep the type of string (μ) and the tension in the string (T) the same and move the vibration transducer towards or away from the pulley by an set length measured using the meter rule. Each time, find the new first harmonic frequency and length of the string between the vibration transducer and pulley and record both. Then, plot f against l

Alternately, keep μ and L the same but change T by adding a new mass, calculating the new tension, calculating the new first harmonic, recording both, and adding a new mass. Then, plot T against f

Keep both T and L the same, but vary μ using a new string each time. Measure the first harmonic frequency of each string and plot f against μ in ascending order of μ

How does altering L, μ and T affect the resonant frequency of a string.

The larger L is, the lower the resonant frequency, as the length of a half wavelengths is larger. The larger μ lower resonant frequency waves travel slower. Looser string - lower resonant frequency as waves travel slower

What is the equation for the frequency of the first harmonic

Describe amplitude of particles on a standing wave

Amplitude varies from 0 at the nodes to maximum at the antinodes

What is diffraction?

The spread of waves as they go round an obstacle or come through a narrow gap

What is the amount of diffraction dependent on?

Size of gap relative to wavelength

-gap > wavelength by large amount, no noticeable diffraction

- noticeable diffraction through gap several wavelengths wide

- most diffraction if gap = wavelength

- if gap < wavelength, waves mostly reflected back

How do you form a diffraction pattern with light through a slit?

Shine monochromatic (same wavelength), coherent light through a slit the same size as the wavelength of said light, you will see a central bright fringe followed by patterns of dark and light fringes

What happens when white light is diffracted?

The fringes are now all different spectra of colours, as white light is made up of many different wavelengths

What does intensity of light mean?

The number of photons hitting any given spot. Calculated with power per unit area or p/m²

Why is light brightest at the central maximum

The intensity of the light is highest there

How do you vary the central maximum with wavelengths and slit size?

Increasing slit width decreases diffraction, so the central maximum is thinner and brighter. Increasing wavelength increases diffraction, so the central maximum is larger and dimmer

How do you demonstrate two source inteference in sound and water?

Two coherent sources of waves (wavelength and frequency are the same) by attaching either two speakers or two vibrators to the same oscillator, and observing the interference patterns

How do you demonstrate two source interference with light?

YOUNG’S DOUBLE SLIT EXPERIMENT

Place a screen in front of two equally spaced slits

Shine a laser (coherent and monochromatic) through said slits. The wavelength of the laser light should be the same as the width of the slits so the light is diffracted

Slits now act as two coherent light sources. A pattern of light and dark fringes are formed on the screen. Thomas young used a lamp rather than a laser

Safety precautions you should take when using lasers:

Safety goggles

Do not shine towards a person

Avoid shining to a reflective surface

Use a warning sign

Turn laser off when not in use

What is young’s double slit formula?

Fringe spacing (w) = λD/s where s is spacing between slits, D is distance between slits and fringes and λ is wavelength

How do you measure fringe spacing

Measure across several fringes then divide by the number of fringe widths between them

What theory did Young’s double slit experiment dethrone and why

Newton believed light was made up of particles called corpuscles. These explained reflection and refraction, but could not explain diffraction and interference.

If it could be shown light had interference patterns then light could be firmly put as a wave. Young’s double slit experiment proved this

What is the wave equation?

Frequency = speed of wave/wavelengths

What does diffracting through more slits do to the interference patterns?

Bright fringes become narrower and brighter and dark fringes become darker

What are the different orders of light?

Diffraction gratings give sharp maxima (lines of light). The central line of maximal brightness is called the zero order line. The lines either side are called the first order lines, and the pair further out from them are called the second order and so on and so forth

What is the equation linking the angle from the central maxima, the distance of slits in a grating, the wavelength and the nth order of light

Sinθd=nλ

How do you derive the equation linking wavelength, angle from the normal, order of wavelength and slit grating distance

1. The distance between a point of interference and the source will be an integer. This point will form a right angled triangle, with the hypotenuse being the distance between two slits and the opposite being an integer multiple of the wavelength of the wave. This is a similar triangle to the one that is formed between the n order maxima, the central maximum and the distance between the central order maximum and the n order maxima. This means that the angle calculated using sin theta=d/n(wavelengths) is the same angle between the central order maximum and n order maxima.

What conclusions can you draw from dsinθ=nλ

If the wavelength is bigger, then for any given diffraction grating sinθ is also bigger so θ is bigger. So the larger the wavelength, the more spread the pattern is

If d is larger, sinθ gets smaller, so the coarser the grating the closer the order maxima

Sinθ>1 is impossible, so if for any given n you get sinθ>1, that order does not exist

What are uses of diffraction gratings

-Light forms a spectrum at each order maxima with red on the inside and purple on the outside, and as chemists and astronomers need to use spectra to identify elements, they use diffraction gratings as they are more accurate than prisms

-The wavelengths of x rays is similar to the distance between atoms in crystalline solids, so if they are shone through crystalline solids diffraction patterns emerge. This acts as diffraction grating, and the pattern that emerges can be used to calculate aperture width (spacing between atoms). This is X ray crystallography and was used to find the structure of DNA