A constant frequency signal from a signal generator is fed to two loudspeakers placed $1.5 \mathrm{m}$ apart. A student, who is $8.0 \mathrm{m}$ away from the loudspeakers, walks across in a line parallel to the line between the loudspeakers. The student measures the distance between successive spots of loudness to be $1.2 \mathrm{m}$. Calculate:

(b) The frequency of the sound (assume the speed of sound is $330 \mathrm{m}{ \mathrm{s}}^{-1}$)

One of the spectral lines from a hydrogen discharge lamp has wavelength $656 \mathrm{nm}$. This light is incident normally at a diffraction grating with $5000$ lines ${\mathrm{cm}}^{-1}$.

Calculate the angles for the first- and second-order maxima for this light

(b) In a double-slit experiment, yellow light of wavelength $590 \mathrm{nm}$ from a sodium discharge tube is used. A student sets up a screen $1.8 \mathrm{m}$ from the double-slit. The distance between $12$ bright fringes is measured to be $16.8 \mathrm{mm}$.

Calculate the separation of the slits.

(c) Describe the effect of:

(i) Using slits of narrower width, but with the same separation

(c) Describe the effect of:

(ii) Using slits with a smaller separation, but of the same width.

(a) A laser light is described as producing light that is both highly coherent and highly monochromatic.

Explain what is meant by the terms coherent and monochromatic.

(b) This diagram shows the experimental setup (left) used to analyse the spectrum of a sodium discharge lamp with a diffraction grating with $500$ lines ${\mathrm{mm}}^{-1}$, and the spectral lines observed (right) in the developed photographic film.

(i) Explain why two spectra are observed.