EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100546310
Author: Jewett
Publisher: CENGAGE L
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Chapter 38, Problem 38.27P

Consider an array of parallel wires with uniform spacing of 1.30 cm between centers. In air at 20.0°C, ultrasound with a frequency of 37.2 kHz from a distant source is incident perpendicular to the array. (a) Find the number of directions on the other side of the array in which there is a maximum of intensity. (b) Find the angle for each of these directions relative to the direction of the incident beam.

(a)

Expert Solution
Check Mark
To determine
The number of directions on the other side of the array for maximum intensity.

Answer to Problem 38.27P

The number of directions on the other side of the array for maximum intensity is three.

Explanation of Solution

Given info: Temperature of air is 20.0°C , spacing between centre is 1.30cm and frequency of array is 37.2kHz .

The wavelength for a diffraction grating can be given as,

λ=vf

Here,

λ is the wavelength of light.

v is the speed of sound.

f is the frequency of the array.

Substitute 343m/s for v and 37.2kHz for f in the above equation to find λ ,

λ=(343m/s)(37.2kHz)(103Hz1kHz)=9.22×103m

The condition for the bright fringe in diffraction can be given as,

mλ=dsinθ (1)

Here,

θ is the angle of spectral line.

λ is the wavelength of light.

m is the order of diffraction.

d is the spacing between centre.

Substitute 90° for θ , 9.22×103m for λ and 1.30cm for d in the equation (1),

m(9.22×103m)=[(1.30cm)(1m100cm)]sin90°m=1.411

The maximum number of direction possible can be given as,

mmax=2m+1

Here,

mmax is the maximum number of directions.

Substitute 1 for m in the above equation,

mmax=2(1)+1=3

Thus, the number of directions on the other side of the array for maximum intensity is three.

Conclusion:

Therefore, the number of directions on the other side of the array for maximum intensity is three.

(b)

Expert Solution
Check Mark
To determine
The angle for each of the directions relative to the direction of the incident beam.

Answer to Problem 38.27P

The angle for each of the directions relative to the direction of the incident beam is 0° , +45.2° and 45.2° .

Explanation of Solution

Given info: Temperature of air is 20.0°C , spacing between centre is 1.30cm and frequency of array is 37.2kHz .

The condition for a diffraction grating as in equation (1) can be given as,

mλ=dsinθ

Rearrange the above expression for θ ,

θ=sin1(mλd) (2)

Substitute (2) for m , 9.22×103m for λ and 1.30cm for d in the equation (2),

θ=sin1((2)(9.22×103m)(1.30cm)(1m100cm))=sin1(1.418)

As the range of sine function is [1,1] , the value of sin1(1.418) is undetermined. Therefore, |m| cannot be more than unity.

Substitute (1) for m , 9.22×103m for λ and 1.30cm for d in the equation (2),

θ=sin1((1)(9.22×103m)(1.30cm)(1m100cm))=sin1(0.709)=45.2°

Thus, θ is (45.2°) for the (1) order of diffraction.

Substitute 0 for m , 9.22×103m for λ and 1.30cm for d in the equation (2),

θ=sin1((0)(9.22×103m)(1.30cm)(1m100cm))=sin1(0)=0°

Thus, θ is 0° for the 0 order of diffraction.

Substitute (1) for m , 9.22×103m for λ and 1.30cm for d in the equation (2),

θ=sin1((1)(9.22×103m)(1.30cm)(1m100cm))=sin1(0.709)=45.2°

Thus, θ is 45.2° for the (1) order of diffraction.

Conclusion:

Therefore, the angle for each of the directions relative to the direction of the incident beam is 0° , +45.2° and 45.2° .

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Chapter 38 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 38 - A Fraunhofer diffraction pattern is produced on a...Ch. 38 - Consider a wave passing through a single slit....Ch. 38 - Assume Figure 38.1 was photographed with red light...Ch. 38 - If plane polarized light is sent through two...Ch. 38 - Why is it advantageous to use a large-diameter...Ch. 38 - What combination of optical phenomena causes the...Ch. 38 - Prob. 38.10OQCh. 38 - When unpolarized light passes through a...Ch. 38 - Off in the distance, you see the headlights of a...Ch. 38 - Prob. 38.1CQCh. 38 - Holding your hand at arms length, you can readily...Ch. 38 - Prob. 38.3CQCh. 38 - (a) Is light from the sky polarized? (b) Why is it...Ch. 38 - Prob. 38.5CQCh. 38 - If a coin is glued to a glass sheet and this...Ch. 38 - Fingerprints left on a piece of glass such as a...Ch. 38 - A laser produces a beam a few millimeters wide,...Ch. 38 - Prob. 38.9CQCh. 38 - John William Strutt, Lord Rayleigh (1842-1919),...Ch. 38 - Prob. 38.11CQCh. 38 - Prob. 38.12CQCh. 38 - Light of wavelength 587.5 nm illuminates a slit of...Ch. 38 - Heliumneon laser light ( = 632.8 nm) is sent...Ch. 38 - Sound with a frequency 650 Hz from a distant...Ch. 38 - A horizontal laser beam of wavelength 632.8 nm has...Ch. 38 - Coherent microwaves of wavelength 5.00 cm enter a...Ch. 38 - Light of wavelength 540 nm passes through a slit...Ch. 38 - A screen is placed 50.0 cm from a single slit,...Ch. 38 - A screen is placed a distance L from a single slit...Ch. 38 - Assume light of wavelength 650 nm passes through...Ch. 38 - What If? Suppose light strikes a single slit of...Ch. 38 - A diffraction pattern is formed on a screen 120 cm...Ch. 38 - Coherent light of wavelength 501.5 nm is sent...Ch. 38 - Prob. 38.13PCh. 38 - The pupil of a cats eye narrows to a vertical slit...Ch. 38 - The angular resolution of a radio telescope is to...Ch. 38 - A pinhole camera has a small circular aperture of...Ch. 38 - The objective lens of a certain refracting...Ch. 38 - Yellow light of wavelength 589 nm is used to view...Ch. 38 - What is the approximate size of the smallest...Ch. 38 - A heliumneon laser emits light that has a...Ch. 38 - To increase the resolving power of a microscope,...Ch. 38 - Narrow, parallel, glowing gas-filled tubes in a...Ch. 38 - Impressionist painter Georges Seurat created...Ch. 38 - A circular radar antenna on a Coast Guard ship has...Ch. 38 - Prob. 38.25PCh. 38 - Prob. 38.26PCh. 38 - Consider an array of parallel wires with uniform...Ch. 38 - Three discrete spectral lines occur at angles of...Ch. 38 - The laser in a compact disc player must precisely...Ch. 38 - A grating with 250 grooves/mm is used with an...Ch. 38 - A diffraction grating has 4 200 rulings/cm. On a...Ch. 38 - The hydrogen spectrum includes a red line at 656...Ch. 38 - Light from an argon laser strikes a diffraction...Ch. 38 - Show that whenever white light is passed through a...Ch. 38 - Light of wavelength 500 nm is incident normally on...Ch. 38 - A wide beam of laser light with a wavelength of...Ch. 38 - Prob. 38.37PCh. 38 - Prob. 38.38PCh. 38 - Potassium iodide (Kl) has the same crystalline...Ch. 38 - Prob. 38.40PCh. 38 - Prob. 38.41PCh. 38 - Why is the following situation impossible? A...Ch. 38 - Prob. 38.43PCh. 38 - The angle of incidence of a light beam onto a...Ch. 38 - Unpolarized light passes through two ideal...Ch. 38 - Prob. 38.46PCh. 38 - You use a sequence of ideal polarizing niters,...Ch. 38 - An unpolarized beam of light is incident on a...Ch. 38 - The critical angle for total internal reflection...Ch. 38 - For a particular transparent medium surrounded by...Ch. 38 - Three polarizing plates whose planes are parallel...Ch. 38 - Two polarizing sheets are placed together with...Ch. 38 - In a single-slit diffraction pattern, assuming...Ch. 38 - Laser light with a wavelength of 632.8 nm is...Ch. 38 - Prob. 38.55APCh. 38 - Prob. 38.56APCh. 38 - Prob. 38.57APCh. 38 - Two motorcycles separated laterally by 2.30 m are...Ch. 38 - The Very Large Array (VLA) is a set of 27 radio...Ch. 38 - Two wavelengths and + (with ) are incident on...Ch. 38 - Review. A beam of 541-nm light is incident on a...Ch. 38 - Prob. 38.62APCh. 38 - Prob. 38.63APCh. 38 - Prob. 38.64APCh. 38 - Prob. 38.65APCh. 38 - Prob. 38.66APCh. 38 - Prob. 38.67APCh. 38 - A pinhole camera has a small circular aperture of...Ch. 38 - Prob. 38.69APCh. 38 - (a) Light traveling in a medium of index of...Ch. 38 - The intensity of light in a diffraction pattern of...Ch. 38 - Prob. 38.72APCh. 38 - Two closely spaced wavelengths of light are...Ch. 38 - Light of wavelength 632.8 nm illuminates a single...Ch. 38 - Prob. 38.75CPCh. 38 - A spy satellite can consist of a large-diameter...Ch. 38 - Suppose the single slit in Figure 38.4 is 6.00 cm...Ch. 38 - In Figure P37.52, suppose the transmission axes of...Ch. 38 - Consider a light wave passing through a slit and...
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