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18 December, 22:10

A submarine is attempting to detect an aircraft carrier transiting the Straits of Malacca. The aircraft carrier has a source level of 90 dB. The submarine's passive sonar has a directivity index of 20 dB and a detection threshold of 15 dB. Biological noise in the Straits is 54 dB. The submarine's self noise is 50 dB. Given that TL = 10 log r, where r is the range in yards (we will show you where this comes from soon), at what range can the carrier just be detected?

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  1. 18 December, 22:16
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    7.94 yards

    Explanation:

    Given:

    Source level = 90 dB

    Directivity index = 20 dB

    Detection threshold = 15 dB

    Biological noise in the Straits = 54 dB

    submarine's self noise = 50 dB

    TL = 10 log r

    where r is the range in yards

    Now,

    Passive sonar equation is given as:

    Detection threshold = Source level - TL - (Noise level - Directivity index)

    Also,

    Noise level = Biological noise in the Straits + submarine's self noise

    or

    Noise level = 54 dB + 50 dB = 104 dB

    Thus, we have

    15 dB = 90 dB - TL - (104 dB - 20 dB)

    or

    TL = 9 dB

    also, we have

    TL = 10 * log r

    thus,

    9 = 10 * log r

    or

    log r = 0.9

    taking anti log both sides, we get

    r = 7.94 yards
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