Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 25, Problem 89P
To determine

The frequency of the broadcast.

Expert Solution & Answer
Check Mark

Answer to Problem 89P

The frequency of the broadcast is 1530kHz.

Explanation of Solution

Sketch the diagram showing the distances.

Physics, Chapter 25, Problem 89P

Find the distance d from the figure using Pythagoras theorem.

    d=(102km)2+h2                                                                             (I)

Here, d is the distance between the lane and the coast guard and h is the height of the plane.

Find the equation for wavelength using equation (I).

    mλ=Δl=(102km)2+h2+h102kmλ=(102km)2+h2+h102kmm                                                        (II)

Here, m is the integer, Δl is the path difference and λ is the wavelength.

Find the equation for frequency.

    f=cλ                                                                                                  (III)

Here, f is the frequency and c is the speed of light.

Conclusion:

Substitute 780m for h and m1 for m in equation (II) to find λ.

    λ=(102km)2+(780m)2+780m102kmm1=((102km)(103m1km))2+(780m)2+780m(102km)(103m1km)m1=783mm1        (IV)

Substitute 975m for h and m2 for m in equation (II) to find λ.

    λ=(102km)2+(975m)2+975m102kmm2=((102km)(103m1km))2+(975m)2+975m(102km)(103m1km)m2=980mm2           (V)

Substitute 1170m for h and m3 for m in equation (II) to find λ.

    λ=(102km)2+(1170m)2+1170m102kmm3=((102km)(103m1km))2+(1170m)2+1170m(102km)(103m1km)m3=1170mm3       (VI)

Find the ratio m2m1 from equations (IV) and (V).

    m2m1=980m783m=54                                                                                               (VII)

Find the ratio m3m1 from equations (V) and (VI).

    m3m1=1177m783m=64                                                                                              (VIII)

From equations (VII) and (VIII), the value of m1 is 4.

Substitute 4 for m1 in equation (IV) to find λ.

    λ=783m4=196m

Substitute 196m for λ and 3.00×108m/s for c in equation (III) to find f.

    f=3.00×108m/s196m=(1530000Hz)(103kHz1Hz)=1530kHz

Thus, the frequency of the broadcast is 1530kHz.

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Chapter 25 Solutions

Physics

Ch. 25.7 - Prob. 25.8PPCh. 25.8 - Prob. 25.9PPCh. 25 - Prob. 1CQCh. 25 - Prob. 2CQCh. 25 - Prob. 3CQCh. 25 - Prob. 4CQCh. 25 - Prob. 5CQCh. 25 - Prob. 6CQCh. 25 - Prob. 7CQCh. 25 - Prob. 8CQCh. 25 - Prob. 9CQCh. 25 - Prob. 10CQCh. 25 - Prob. 11CQCh. 25 - 12. In Section 25.3 we studied interference due to...Ch. 25 - Prob. 13CQCh. 25 - Prob. 14CQCh. 25 - Prob. 15CQCh. 25 - Prob. 16CQCh. 25 - Prob. 17CQCh. 25 - Prob. 18CQCh. 25 - Prob. 19CQCh. 25 - Prob. 20CQCh. 25 - Prob. 21CQCh. 25 - Prob. 1MCQCh. 25 - Prob. 2MCQCh. 25 - Prob. 3MCQCh. 25 - Prob. 4MCQCh. 25 - Prob. 5MCQCh. 25 - Prob. 6MCQCh. 25 - 7. Coherent light of a single frequency passes...Ch. 25 - Prob. 8MCQCh. 25 - Prob. 9MCQCh. 25 - Prob. 10MCQCh. 25 - Prob. 1PCh. 25 - Prob. 2PCh. 25 - Prob. 3PCh. 25 - Prob. 4PCh. 25 - Prob. 5PCh. 25 - Prob. 6PCh. 25 - Prob. 7PCh. 25 - Prob. 8PCh. 25 - Prob. 9PCh. 25 - Prob. 10PCh. 25 - Prob. 11PCh. 25 - Prob. 12PCh. 25 - Prob. 13PCh. 25 - Prob. 14PCh. 25 - Prob. 15PCh. 25 - 16. A transparent film (n = 1.3) is deposited on a...Ch. 25 - 17. A camera lens (n = 1.50) is coated with a thin...Ch. 25 - 18. A soap film has an index of refraction n =...Ch. 25 - Prob. 19PCh. 25 - Prob. 20PCh. 25 - Prob. 21PCh. 25 - Prob. 22PCh. 25 - Prob. 23PCh. 25 - Prob. 24PCh. 25 - Prob. 25PCh. 25 - Prob. 26PCh. 25 - Prob. 27PCh. 25 - Prob. 36PCh. 25 - Prob. 28PCh. 25 - Prob. 32PCh. 25 - Prob. 29PCh. 25 - Prob. 30PCh. 25 - Prob. 31PCh. 25 - Prob. 34PCh. 25 - Prob. 33PCh. 25 - Prob. 35PCh. 25 - Prob. 37PCh. 25 - Prob. 38PCh. 25 - Prob. 39PCh. 25 - Prob. 40PCh. 25 - Prob. 41PCh. 25 - Prob. 42PCh. 25 - Prob. 43PCh. 25 - 44. ✦ White light containing wavelengths from 400...Ch. 25 - Prob. 45PCh. 25 - Prob. 46PCh. 25 - 47. The central bright fringe in a single-slit...Ch. 25 - Prob. 48PCh. 25 - Prob. 49PCh. 25 - Prob. 50PCh. 25 - Prob. 51PCh. 25 - Prob. 52PCh. 25 - Prob. 53PCh. 25 - Prob. 54PCh. 25 - Prob. 55PCh. 25 - Prob. 56PCh. 25 - Prob. 57PCh. 25 - Prob. 58PCh. 25 - Prob. 60PCh. 25 - Prob. 61PCh. 25 - Prob. 59PCh. 25 - Prob. 62PCh. 25 - 63. ✦ If you shine a laser with a small aperture...Ch. 25 - Prob. 64PCh. 25 - Prob. 65PCh. 25 - Prob. 66PCh. 25 - Prob. 67PCh. 25 - Prob. 68PCh. 25 - Prob. 69PCh. 25 - 70. Coherent green light with a wavelength of 520...Ch. 25 - Prob. 71PCh. 25 - Prob. 72PCh. 25 - Prob. 73PCh. 25 - Prob. 74PCh. 25 - Prob. 75PCh. 25 - Prob. 76PCh. 25 - Prob. 77PCh. 25 - Prob. 78PCh. 25 - Prob. 91PCh. 25 - Prob. 79PCh. 25 - Prob. 80PCh. 25 - Prob. 81PCh. 25 - Prob. 82PCh. 25 - Prob. 83PCh. 25 - Prob. 84PCh. 25 - Prob. 85PCh. 25 - Prob. 86PCh. 25 - Prob. 87PCh. 25 - Prob. 88PCh. 25 - Prob. 89PCh. 25 - Prob. 90PCh. 25 - Prob. 93PCh. 25 - Prob. 92PCh. 25 - Prob. 94PCh. 25 - Prob. 95PCh. 25 - Prob. 96PCh. 25 - Prob. 97P
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