KVPY SX SB Exam 2016 Question Paper

Question : 39 of 120

Marks: +1, -0

A hearing test is conducted on an aged person. It is found that her threshold of hearing is 20 decibels at 1 kHz and it rises linearly with frequency to 60 decibels at 9 kHz. The minimum intensity of sound that the person can hear at 5 kHz is-

10 times than that at 1 kHz
100 times than that at 1 kHz
0.5 times than that at 9 kHz
0.05 times than that at 9 kHz

Validate

Solution:

at 5 KHz Hearing capacity = 40 dB
Intensity at 1 KHz

β=10\log(I/I_0)

I=I_0 10^{β/10}

(I)_{1 \KHz} = I_0 10^(20\/10)

= I_0(10)^2

(I)_{5 \KHz} = I_0 10^(40\/10) = I_0(10)^4

(I)_{1\KHz}/(I)_{5\KHz}=1/100

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