Physics-
General
Easy
Question
A sound absorber the sound level by 20 dB. The intensity decreases by a factor of
- 1000
- 10000
- 10
- 100
The correct answer is: 100
Let intensity of sound be I and I’.
Loudness of sound initially
![beta subscript 1 end subscript equals 10 log invisible function application open parentheses fraction numerator I over denominator I subscript 0 end subscript end fraction close parentheses](data:image/png;base64,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)
Later,
![beta subscript 2 end subscript equals 10 log invisible function application open parentheses fraction numerator I to the power of ´ end exponent over denominator I subscript 0 end subscript end fraction close parentheses](data:image/png;base64,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)
Given, ![beta subscript 2 end subscript minus beta subscript 1 end subscript equals 20](data:image/png;base64,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)
![therefore 20 equals log invisible function application open parentheses fraction numerator I to the power of ´ end exponent over denominator I end fraction close parentheses](data:image/png;base64,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)
![I to the power of ´ end exponent equals 100 I](data:image/png;base64,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)
Related Questions to study
Physics-
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
Physics-General
Physics-
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
![](data:image/png;base64,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)
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
![](data:image/png;base64,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)
Physics-General
Physics-
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
Physics-General
Physics-
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,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)
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,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)
Physics-General
Physics-
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
Physics-General
Physics-
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
Physics-General
Physics-
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
Physics-General
Physics-
If you set up the seven overtone on a string fixed at both ends, how many nodes and antinodes are set up in it?
If you set up the seven overtone on a string fixed at both ends, how many nodes and antinodes are set up in it?
Physics-General
Physics-
If in a resonance tube a oil of density higher than that water is used then at the resonance frequency would
If in a resonance tube a oil of density higher than that water is used then at the resonance frequency would
Physics-General
Physics-
Two vibrating tuning forks produce progressive waves given by
. Number of beats produced per minute is
Two vibrating tuning forks produce progressive waves given by
. Number of beats produced per minute is
Physics-General
Chemistry-
Silica reacts with magnesium compound X, X reacts with dil HCl and forms Y and Z If two moles of HCl reacts with one mole of X then how many mole of y will be formed
Silica reacts with magnesium compound X, X reacts with dil HCl and forms Y and Z If two moles of HCl reacts with one mole of X then how many mole of y will be formed
Chemistry-General
Chemistry-
Carbondioxide is used for extinguishing fire because
Carbondioxide is used for extinguishing fire because
Chemistry-General
Chemistry-
Which is correct regarding CO2
Which is correct regarding CO2
Chemistry-General
Chemistry-
CO2and N2are non-supporters of combustion However for putting out fires CO2 is preferred over N2 because CO2
CO2and N2are non-supporters of combustion However for putting out fires CO2 is preferred over N2 because CO2
Chemistry-General
Chemistry-
The correct statement with respect to CO is
The correct statement with respect to CO is
Chemistry-General