Question

The intensity of a 50-dB whistle is doubled, so what is the new decibel level?

a) 53 dB
b) 56 dB
c) 60 dB
d) 63 dB

Answer 1

When the intensity of a 50-dB whistle is doubled, the new decibel level is approximately 53 dB, due to the nature of the logarithmic decibel scale. The correct option is a).

Step-by-step explanation:

The question asks about the new decibel level when the intensity of a sound measured at 50 dB is doubled. The formula to calculate the new decibel level when the intensity is doubled is:

dB_{new} = dB_{original} + 10 \cdot \log_{10}(2)

Since the logarithm (base 10) of 2 is approximately 0.30103, which can be rounded to 0.3, the calculation will be:

dB_{new} = 50 dB + 10 \cdot 0.3 = 50 dB + 3 dB = 53 dB

Therefore, when doubling the intensity of a 50-dB whistle, the new decibel level is approximately 53 dB. Option a) is the correct one.