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KVPY2016PhysicsWaves and Sound

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-

Options

  1. A10 times than that at 1 kHz .
  2. B100 times than that at 1 kHz
  3. C0.5 times than that at 9 kHz
  4. D0.05 times than that at 9 kHz

Correct answer

B. 100 times than that at 1 kHz

Step-by-step solution

at 5 KHz Hearing capacity =40 ~dB Intensity at 1 KHz array l =10 ( I I ₀ ) I = I ₀ 10^ ( 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 array

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