Q88 of 118 Page 352

A small source of sound S of frequency 500 Hz is attached to the end of a light string and is whirled in a vertical circle of radius 16 m. The string just remains tight when the source is at the highest point. (a) An observer is located in the same vertical plane at a large distance and at the same height as the center of the circle (figure 16-E13). The speed of sound in air = 330 m s-1 and g = 10 m s-2. Find the maximum frequency heard by the observer. (b) An observer is situated at a large distance vertically above the center of the circle. Find the frequencies heard by the observer corresponding to the sound emitted by the source when it is at the same height as the center.


(a)


Here the moving part is the source. So, the frequency heard is solely dependent on the speed of the source. This is given by,




So, the frequency will be increasing when the source is coming towards and will be the maximum when it reaches B.



So, the frequency will become,





(b) 490 Hz and 511 Hz


The velocity at the points mentioned in the question is,



The frequencies will become,




Similarly,




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Figure (16-E12) shows a source of sound moving along the X-axis at a speed of 22 m s continuously emitting a sound of frequency 2-0 kHz which travels in air at a speed of 330 m s-1. A listener Q stands on the Y-axis at a distance of 330 m from the origin. At t = 0, the source crosses the origin P. (a) When does the sound emitted from the source at P reach the listener Q? (b) What will be the frequency heard by the listener at this instant? (c) Where will the source be at this instant?


 86

A source emitting sound at frequency 4000 Hz, is moving along the Y-axis with a speed of 22 m s-1, A listener is situated on the ground at the position (660 m, 0). Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of sound in air = 330 m s-1.

 87

A source of sound emitting a 1200 Hz note travels along a straight line at a speed of 170 m s-1. A detector is placed at a distance of 200 m from the line of motion of the source. (a) Find the frequency of sound received by the detector at the instant when the source gets closest to it. (b) Find the distance between the source and the detector at the instant it detects the frequency 1200 Hz. Velocity of sound in air = 340 m s-1.

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A source emitting a sound of frequency v is placed at a large distance from an observer. The source stats moving towards the observer with a uniform acceleration a. Find the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is u.