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Question

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

  1. pR    
  2. pR/2    
  3. pR/4    
  4. all of these    

The correct answer is: all of these

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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

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