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Chapter 36: Q32P (page 1111)

(a) A circular diaphragm 60 cm in diameter oscillates at a frequency of 25 kHz as an underwater source of sound used for submarine detection. Far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. Take the speed of sound in water to be 1450 m/s and find the angle between the normal to the diaphragm and a line from the diaphragm to the first minimum. (b) Is there such a minimum for a source having an (audible) frequency of 1.0 kHz?

Short Answer

Expert verified
  1. The required angle is 6.77掳.
  2. There is no minimum for a source having a frequency of 1kHz.

Step by step solution

01

Concept/Significance of first minima in diffraction pattern

For the first minima in diffraction pattern, the diffraction angle is given by,

sin胃=1.22位d胃=sin-1(1.22位d)......(1)

02

(a) Find the angle between the normal to the diaphragm and a line from the diaphragm

Find the wavelength as follows.

位=vf=145025脳103=0.058m

Substitute0.6m for dand 0.058mfor 位in equation (1).

胃=sin-11.220.058m0.6m胃=sin-10.1179胃=6.77掳

Therefore, the required angle is胃=6.77掳 .

03

(b) Find whether the minimum is possible or not

Find the wavelength as follows.

位=vf=14501脳103=1.45m

Substitute 0.6mford and1.45m for位 in equation (1).

sin胃=1.221.45m0.6msin胃=2.95>1

It is known thatsin胃>1 is not possible. So, no minima are possible.

Therefore, there is no minimum for a source having a frequency of1kHz .

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Most popular questions from this chapter

(a) Figure 36-34a shows the lines produced by diffraction gratingsA and B using light of the same wavelength; the lines are of the same order and appear at the same angles 胃. Which grating has the greater number of rulings? (b) Figure 36-34b shows lines of two orders produced by a single diffraction grating using light of two wavelengths, both in the red region of the spectrum. Which lines, the left pair or right pair, are in order with greater m? Is the center of the diffraction pattern located to the left or to the right in(c) Fig. 36-34a andd) Fig. 36-34b?

An acoustic double-slit system (of slit separation dand 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 2蟺. Take both interference and diffraction effects into account.

When monochromatic light is incident on a slit 22.0 渭m wide, the first diffraction minimum lies at 1.80掳 from the direction of the incident light. What is the wavelength?

The distance between the first and fifth minima of a single slit diffraction pattern is 0.35mmwith the screen 40cmaway from the slit, when light of wavelength role="math" localid="1663070418419" 550nmis used. (a) Find the slit width. (b) Calculate the angle role="math" localid="1663070538179" 胃 of the first diffraction minimum.

A beam of light consisting of wavelengths from460.0nmto640.0nmis directed perpendicularly onto a diffraction grating with 160 lines/mm. (a) What is the lowest order that is overlapped by another order? (b) What is the highest order for which the complete wavelength range of the beam is present? In that highest order, at what angle does the light at wavelength (c)460.0nmand (d) 640.0nmappear? (e) What is the greatest angle at which the light at wavelength460.0nmappears?
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