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Chapter 33: Q. 42 (page 956)

Because sound is a wave, it's possible to make a diffraction grating for sound from a large board of sound-absorbing material with several parallel slits cut for sound to go through. When 10kHzsound waves pass through such a grating, listeners 10mfrom the grating report "loud spots" 1.4mon both sides of center. What is the spacing between the slits? Use 340msfor the speed of sound.

Short Answer

Expert verified

The Speed of sound in slits spacing is,d=24.5cm.

Step by step solution

01

Step: 1 Grating:

A diffracted is an optical device that splits (disperses) light that is made up of several distinct wavelengths (e.g., white light) into light components by wavelength. A grating with a large number of uniformly spaced parallel slits is the most basic variation.

02

Step: 2 Equating equation:

Grating equation as

Y1=Ltan鈦�胃1胃1=tan鈭�1鈦�Y1Ldsin鈦�胃m=m位

Spacing parameter as

d=m位sin鈦�tan鈭�1鈦�Y1Ld=mv谓sin鈦�tan鈭�1鈦�Y1L.

03

Step: 3 Slit spacing:

The spacing as

d=1脳3401脳104脳sin鈦�tan鈭�1鈦�1.410d=0.245md=24.5cm.

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Most popular questions from this chapter

Light from a helium-neon laser (位=633nm)illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen 50cmbehind the aperture matches the diameter of the geometric image. What is the aperture's diameter (in mm)?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0kmin diameter. Staying within this diameter is accomplished by using a special large diameter laser. If 位=532nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is384,000km.

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. FringeCis the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" 500nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

FIGURE shows the light intensity on a screen 2.5mbehind an aperture. The aperture is illuminated with light of wavelength 620nm.

a. Is the aperture a single slit or a double slit? Explain.

b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

White light400-700nmincident on a 600line/mmdiffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen 2.0mbehind the grating?
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