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InterviewSolution
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What are beats ? Obtain an expression for the beat frequency ? Where and howare beatsmade us of ? |
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Answer» Solution :Beats `:` Two sound waves of nearly same frequency are travelling in the same direction and interfere to produce a regular waxing and waning in the intensity of the resultant sound waves at regular intervals of time are called Beats. If `v_(1)` and `v_(2)` are the frequencies of two sound notessuperimposed ALONG the same direction, no of beats heard per second `= Delta v = v_(1)- v_(2)` . Maximumno. of beats heard per heard persec is 10 due to persistence of hearing . Expression for the beat frequency `:` (1) Consider the two wave trains of equal amplitudebut of nearlyequal frequencies . (2) Let the frequencies of the waves be `v_(1)` and `v_(2)`. SAY `v_(1)` is slightly greater than `v_(2)`. (3) Let the beatperiod be T seconds. (4)No.of vibrations , made by the firstwave train in T seconds `= v_(1)T ` `[ :'` no. of oscillations in 1 sec = v] `[ :'` no. of oscillationsin T sec = vt ] (5) No. ofvibrations ,made by the second wave train inT secons =`v_(2) T ` (6)During the timeinterval T, the first wave trainwould have completed one vibration more than the second wave train. (7) Hence, `v_(1)T -v_(2)T = 1 ` or`v_(1) - v_(2)= (1)/(T )` (8) Since, T is the beat period, no.of beats per seconds`= (1)/(T )` (9) Hence the beatfrequency `= (1)/( T ) = v_(1) - v_(2) = Deltav ` (10)That is the beat frequency is the difference between the frequencies of the two wave trains. PRACTICAL applications of beats `:` (i) Determinationof an unknown frequency `:` Out of two tunning forks, one is loaded with wax and the other is filled. Theexcited tunning forks are close together and no. of beats can be heard.Then after unknownfrequencies of them will be found practically. (ii) For tuning musical instruments `:` Musicians use the beatphenomenon in tuning their musicalinstruments. (III) For producing COLOURFUL effects in music`:` Sometimes , a rapid succession of beats is knowingly introduced in music . This produces an effect similarto that of human voice and is appreciated by the audience. (iv) For detection of Marsh gas ( dangerous gases) in mines. |
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