To determine To find : The time required for the sound intensity level heard by the gardener to increase by 10.0 dB . Explanation Given data: A portable radio is sitting at the edge of a balcony 5.1 m above the ground. The unit is emitting the sound uniformly in all directions. By an accident, the radio falls from the balcony and continue to play on the way down. A gardener is working in a flower bed directly below the falling unit. Formula used: Consider the sound intensity level at the initial position (edge of the balcony), and at the final position (ground) of the radio as β i , and β f respectively. Refer to the equation (16.10) in the textbook, and modify the expression for sound intensity level at the initial position of the radio as follows. β i = ( 10 dB ) log ( I i I 0 ) (1) Here, I i is the sound intensity at the initial position of the radio, and I 0 is the intensity of the reference level, which is 1.0 × 10 − 12 W m 2 . Refer to the equation (16.10) in the textbook, and modify the expression for sound intensity level at the final position of the radio as follows. β f = ( 10 dB ) log ( I f I 0 ) (2) Here, I f is the sound final at the initial position of the radio Consider the height (distance) between the radio (source) and the gardener (observer) as h i when the radio at its initial position, which is given as 5.1 m. Consider the height between the radio and the gardener as h f when the radio at its final position. Refer to the equation (16.9) in the textbook, and modify the expression for sound intensity at the initial position of the radio as follows. I i = P 4 π ( h i ) 2 (3) Here, P is the power radiated from the radio, which is equal at all points (since the radio emits the sound uniformly in all the directions). Refer to the equation (16.9) in the textbook, and modify the expression for sound intensity at the final position of the radio as follows. I f = P 4 π ( h f ) 2 (4) From the given data, the sound intensity level increased to 10.0 dB when the radio falls to ground from the balcony. Therefore, write the expression as follows. β f − β i = 10.0 dB (5) Calculation of height between the radio and the gardener when the radio at its final position ( h f ) : From the given data, the height between the radio and the gardener when the radio at its initial position is 5.1 m. h i = 5.1 m Subtract equation (1) from equation (2) as follows. β f − β i = ( 10 dB ) log ( I f I 0 ) − ( 10 dB ) log ( I i I 0 ) = ( 10 dB ) [ log ( I f I 0 ) − log ( I i I 0 ) ] = ( 10 dB ) log [ ( I f I 0 ) ( I i I 0 ) ] { ∵ log ( A ) − log ( B ) = log ( A B ) } = ( 10 dB ) log ( I f I i ) From equation (3), and (4), substitute P 4 π ( h i ) 2 for I i , and P 4 π ( h f ) 2 for I f , β f − β i = ( 10 dB ) log [ P 4 π ( h f ) 2

11th Edition

ISBN: 9781119326342

Author: CUTNELL

Publisher: WILEY

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Chapter 16, Problem 73P

To determine

To find: The time required for the sound intensity level heard by the gardener to increase by 10.0 dB .

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Chapter 16, Problem 72P

Chapter 16, Problem 76P

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