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A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generates a wave of intensity I0 which is equally divided into two parts: one part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed

If a minima is formed at the detector then, the magnitude of wavelength of the wave produced is given by

  1. 2 pi R    
  2. fraction numerator 3 over denominator 2 end fraction pi R    
  3. fraction numerator 4 over denominator 5 end fraction pi R    
  4. None of these    

The correct answer is: 2 pi R

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General
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A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generates a wave of intensity I0 which is equally divided into two parts: one part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed

If a maxima is formed at a detector then, the magnitude of wavelength of the wave produced is given by

A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generates a wave of intensity I0 which is equally divided into two parts: one part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed

If a maxima is formed at a detector then, the magnitude of wavelength of the wave produced is given by

Physics-General
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Superposition of waves results in maximum and minimum of intensities such as in case of standing waves. This phenomenon is called as interference. Another type of superposition result in interference in time which is called as beats. In this case waves are analyzed at a fixed point as a function of time. If the two waves are of nearby same frequency are superimposed, at a particular point, intensity of combined waves gives a periodic peak and fall. This phenomenon is beats. If w1 and w2 are the frequencies of two waves then by superimposed y = y1 + y2 , we get at x = 0, y equals open square brackets 2 A c o s invisible function application open parentheses fraction numerator omega subscript 1 end subscript minus omega subscript 2 end subscript over denominator 2 end fraction close parentheses times t close square brackets s i n invisible function application open square brackets fraction numerator omega subscript 1 end subscript plus omega subscript 2 end subscript over denominator 2 end fraction close square brackets times t Thus amplitude frequency is small and fluctuates slowly. A beat i.e., a maximum of intensity occurs, also intensity depends on square of amplitude. The beat frequency is given by omega subscript text beat  end text end subscript equals open vertical bar omega subscript 1 end subscript minus omega subscript 2 end subscript close vertical bar Number of beats per second is called as beat frequency. A normal ear can detect only upto 10 Hz of frequency because of persistence of ear The frequency of beats produced in air when two sources of sound are activated, one emitting wavelength 32 cm, other 32.2 cm is open parentheses text  Take  end text V subscript text soud  end text end subscript equals 350 m divided by s close parentheses

Superposition of waves results in maximum and minimum of intensities such as in case of standing waves. This phenomenon is called as interference. Another type of superposition result in interference in time which is called as beats. In this case waves are analyzed at a fixed point as a function of time. If the two waves are of nearby same frequency are superimposed, at a particular point, intensity of combined waves gives a periodic peak and fall. This phenomenon is beats. If w1 and w2 are the frequencies of two waves then by superimposed y = y1 + y2 , we get at x = 0, y equals open square brackets 2 A c o s invisible function application open parentheses fraction numerator omega subscript 1 end subscript minus omega subscript 2 end subscript over denominator 2 end fraction close parentheses times t close square brackets s i n invisible function application open square brackets fraction numerator omega subscript 1 end subscript plus omega subscript 2 end subscript over denominator 2 end fraction close square brackets times t Thus amplitude frequency is small and fluctuates slowly. A beat i.e., a maximum of intensity occurs, also intensity depends on square of amplitude. The beat frequency is given by omega subscript text beat  end text end subscript equals open vertical bar omega subscript 1 end subscript minus omega subscript 2 end subscript close vertical bar Number of beats per second is called as beat frequency. A normal ear can detect only upto 10 Hz of frequency because of persistence of ear The frequency of beats produced in air when two sources of sound are activated, one emitting wavelength 32 cm, other 32.2 cm is open parentheses text  Take  end text V subscript text soud  end text end subscript equals 350 m divided by s close parentheses

Physics-General
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A traveling wave on stretched string can be understood by the function y = f(x -vt). Here v is the wave speed ‘x’ is co-ordinate of point and ‘y’ is its instantaneous displacement. To describe the wave completely, we must specify the function f. If the wave moves in negative x-direction y (x, t) = f(x + vt) and if it moves in positive x-direction y (x, t) = f(x - vt). The general relation for a traveling wave must satisfy the relation fraction numerator d to the power of 2 end exponent f over denominator d x to the power of 2 end exponent end fraction equals fraction numerator 1 over denominator v to the power of 2 end exponent end fraction times fraction numerator d to the power of 2 end exponent y over denominator d t to the power of 2 end exponent end fraction, if plane wave exists. The particle velocity and wave velocity are related by Vpa = - (slope) (wave velocity ). Answer the following questionsConsider the snapshot of a wave traveling in positive x-direction

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Radio waves coming at angle a to vertical are received by a ladder after reflection from a nearby water surface and also directly. What can be height of antenna from water surface so that it records a maximum intensity (a maxima) (wavelength = l )

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Two coherent narrow slits emitting wave length l in the same phase are placed parallel to each other at a small separation of 2 l , the sound is detected by moving a detector on the screen S at a distance D (>> l ) from the slit S1 as shown in figure.Find the distance x such that the intensity at P is equal to the intensity at O

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Sound from two coherent sources S1 and S2 are sent in phase and detected at point P equidistant from both the sources. Speed of sound in normal air is V0 , but in some part in path S1 , there is a zone of hot air having temperature 4 times, the normal temperature, and width d. What should be minimum frequency of sound, so that minima can be found at P?

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Figure shows two snapshots of medium particles within a time interval of 1/60 s. Find the possible time periods of the wave

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