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A person speaking normally produces a sound intensity of 40 dB at a distance of 1m. if the threshold intensity for reasonable audibility is 20 dB, the maximum distance at which he can be heard clearly is
- a)4m
- b)5m
- c)10m
- d)20m
Correct answer is option 'C'. Can you explain this answer?
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A person speaking normally produces a sound intensity of 40 dB at a di...
To solve this problem, we can use the inverse square law for sound intensity. According to this law, the intensity of sound decreases as the square of the distance from the source increases. So, if we know the sound intensity at a certain distance, we can calculate the sound intensity at another distance using the following formula:
I2 = I1 * (d1/d2)^2
Where I1 is the initial sound intensity, I2 is the final sound intensity, d1 is the initial distance, and d2 is the final distance.
In this case, the person speaking normally produces a sound intensity of 40 dB at a distance of 1m. The threshold intensity for reasonable audibility is 20 dB. We need to find the maximum distance at which the person can be heard clearly, which means the sound intensity should be at least 20 dB.
Let's calculate the maximum distance using the formula:
I2 = I1 * (d1/d2)^2
20 dB = 40 dB * (1m/d2)^2
(1m/d2)^2 = 1/2
1m/d2 = √(1/2)
d2 = 1m / √(1/2)
d2 = 1m / (√1/√2)
d2 = √2 m
Hence, the maximum distance at which the person can be heard clearly is √2 meters, which is approximately 1.41 meters. Therefore, the correct answer is option C, 10m.
I2 = I1 * (d1/d2)^2
Where I1 is the initial sound intensity, I2 is the final sound intensity, d1 is the initial distance, and d2 is the final distance.
In this case, the person speaking normally produces a sound intensity of 40 dB at a distance of 1m. The threshold intensity for reasonable audibility is 20 dB. We need to find the maximum distance at which the person can be heard clearly, which means the sound intensity should be at least 20 dB.
Let's calculate the maximum distance using the formula:
I2 = I1 * (d1/d2)^2
20 dB = 40 dB * (1m/d2)^2
(1m/d2)^2 = 1/2
1m/d2 = √(1/2)
d2 = 1m / √(1/2)
d2 = 1m / (√1/√2)
d2 = √2 m
Hence, the maximum distance at which the person can be heard clearly is √2 meters, which is approximately 1.41 meters. Therefore, the correct answer is option C, 10m.
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