A student in the front row of a concert is at a distance of 2 m from the speaker. They hear the sound at 140dB. What is the sound intensity if the student walks 20 m away. What is the sound intensity at 2 m if there are 100 speakers at the same level at the same time instead of 1.

Question

A student in the front row of a concert is at a distance of 2 m from the speaker. They hear the sound at 140dB. What is the sound intensity if the student walks 20 m away. What is the sound intensity at 2 m if there are 100 speakers at the same level at the same time instead of 1.

Answer 1

To find the sound intensity at different distances, we need to use the inverse square law for sound intensity. According to this law, sound intensity decreases as the square of the distance from the source increases. The formula to calculate sound intensity is:

I2 = I1 × (d1/d2)²

where I1 is the initial sound intensity, d1 is the initial distance, I2 is the new sound intensity, and d2 is the new distance.

1) Sound intensity when the student moves 20 m away:

Given: Initial distance (d1) = 2 m
Initial sound intensity (I1) = 140 dB
New distance (d2) = 20 m

First, we need to convert the decibel (dB) value to sound intensity using the formula:

I = 10^(dB/10)

Substituting the given values:

I1 = 10^(140/10)

Next, we can calculate the new sound intensity (I2) at a distance of 20 m using the inverse square law formula:

I2 = I1 × (d1/d2)²

Substituting the values:

I2 = I1 × (2/20)²

2) Sound intensity at a distance of 2 m if there are 100 speakers:

Given: Initial distance (d1) = 2 m
Initial sound intensity (I1) = 140 dB
Number of speakers (N) = 100

If there are multiple speakers at the same level emitting sound simultaneously, the sound intensity increases. To calculate the sound intensity at a distance of 2 m with 100 speakers instead of one, we need to determine the combined sound intensity contributed by all the speakers.

Using the formula for combined sound intensity:

I_combined = I1 × N

Substituting the given values:

I_combined = I1 × 100

Therefore, to calculate the sound intensity in both scenarios, follow these steps:

1) Calculate the initial sound intensity using the given decibel value:
I1 = 10^(140/10)

2) For the first scenario:
Calculate the new sound intensity at a distance of 20 m using the inverse square law formula:
I2 = I1 × (2/20)²

3) For the second scenario:
Calculate the combined sound intensity emitted by 100 speakers:
I_combined = I1 × 100

A student in the front row of a concert is at a distance of 2 m from the speaker. They hear the sound at 140dB. What is the sound intensity if the student walks 20 m away. What is the sound intensity at 2 m if there are 100 speakers at the same level at the same time instead of 1.

go away

To find the sound intensity at different distances, we need to use the inverse square law for sound intensity. According to this law, sound intensity decreases as the square of the distance from the source increases. The formula to calculate sound intensity is: