Question

Led Zeppelin once played a concert which exerted sounds of 10,000 times the intensity of a sound that can just be heard. What is the loudness in decibels?

Answer 1

The loudness in decibels of the sound exerted by Led Zeppelin, which was 10,000 times more intense than the threshold of hearing, is 100 dB.

Step-by-step explanation:

To calculate the loudness in decibels of a sound exerted by Led Zeppelin that is 10,000 times the intensity of a sound that can just be heard, we can use the formula for sound intensity level:

The sound intensity level L in decibels (dB) is defined as:

L = 10 × log10(I / Io)

Where:

• I is the intensity of the sound we want to measure.
• Io is the reference intensity of the threshold of hearing, which is 10⁻¹² W/m² or 0 dB.

Since every factor of 10 in intensity corresponds to 10 dB increase in loudness, a sound that is 10,000 times more intense than the threshold (10⁴ as intense) would be 100 dB louder than the threshold. Therefore, if the threshold is 0 dB, we add 100 dB to find the loudness:

L = 0 dB + 100 dB = 100 dB

So, the concert played by Led Zeppelin had an intensity level of the sound exerted at 100 dB. This is within the range that can potentially cause hearing damage if exposure is prolonged.