Question

An acoustic double-slit system (of slit separation $\mathit{d}$and slit width ) is driven by two loudspeakers as shown in Fig. 36-51. By use of a variable delay line, the phase of one of the speakers may be varied relative to the other speaker. Describe in detail what changes occur in the double-slit diffraction pattern at large distances as the phase difference between the speakers is varied from zero to $\mathbf{2}\mathbf{\pi }$. Take both interference and diffraction effects into account.

Short answer

The peaks of the sine shift until splits from maximum central to smaller maxima.

Step-by-step solution

Write the given data from the question.

The slit separation is$d$ .

The slit width is$a$ .

Determine the changes occur in the double slit diffraction at large distance.

For the phase difference is $\mathrm{\pi }$, then the reverse of angle,

${\mathit{\theta }}_{\mathbf{R}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{22}\frac{\mathbf{\lambda }}{\mathbf{d}}$

Here, $\lambda$is the wavelength and$d$ is the slit separation.

For the phase difference is varied from $0$to${180}^{°}$ , and${180}^{°}$ to${360}^{°}$ the peaks of the sine shiftcontinuouslyuntil it spilt the maximum central into smaller maxima and located at the angle$\theta$ , which is given by,

.

$a\sin \theta =\pm \lambda$

Hence the peaks of the sine shift until splits from maximum central to smaller maxima.