Q29 of 118 Page 352

Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of one of the speakers as shown in figure (16-E3). Find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 m/s.


Given:


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Distance between the two speakers d = 2.40 m
Speed of sound in air v = 320 m/sec
Frequency of the two stereo speakers f =?


As shown in the figure, the path difference between the sound waves reaching the listener is given by:




Wavelength of either sound wave:



We know that destructive interference will occur if the path difference is an odd integral multiple of the wavelength.


So,







On putting the value of n = 1, 2, 3,…49, the person can hear in the audible region from 20 Hz to 2000 Hz.


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27

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure (16-E1). It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 m/s.


 28

A source S and a detector D are placed at a distance d apart. A big cardboard is placed at a distance √2 d from the source and the detector as shown in figure (16-E2). The source emits a wave of wavelength = d/2 which is received by the detector after reflection from the cardboard. It is found to be in phase with the direct wave received from the source. By what minimum distance should the cardboard be shifted away so that the reflected wave becomes out of phase with the direct wave?


 30

Two sources of sound, S1 and S2, emitting waves of equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to S1S2 and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which the detector should be shifted to detect a minimum of sound.

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 31

Two speakers S1 and S2, driven by the same amplifier, are placed at y = 1.0 m and y = - 1.0 m (figure 16-E4). The speakers vibrate in phase at 600 Hz. A man stands at a point on the X-axis at a very large distance from the origin and starts moving parallel to the Y-axis. The speed of sound in air is 330 m/s. (a) At what angle θ will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (C) If he continues to walk along the line, how many more maxima can he hear?