Five people talk simultaneously. If the intensity level is 70 dB when either one speaks alone, what is the intensity level when both speak at once?

a) Intensity from 1 person = i, from 5 people = 5i, reference level = iₒ

dB = 10 log (i / iₒ)

For 1 person .. 97 = 10 log (i/iₒ) .. log (i/iₒ) = 9.7 .. i /iₒ = 10^9.7 .. .. i = iₒ x 10^9.7

For 5 people .. i' = 5 i .. .. i' = 5 iₒ x 10^9.7..
dB = 10 log (i' / iₒ)
dB = 10 log (5 iₒ x 10^9.7 / iₒ)
dB = 10 log (5 x 10^9.7) .. 10 log (5 x 5.01^9) .. 10 log (2.506^10) .. 10 x 10.39

Total intensity ►= 104 dB .. .. (103.9 dB)

b)
F' = frequency that arrives at insect (source [Vs] moving towards insect)
F'= Vo x Fo / (Vo - Vs)
F' = 340m/s x 60.60kHz / (340m/s - 4.70m/s) .. .. F' = 61.45 kHz

F'' = frequency received by bat moving [Vr] towards stationary source F' (reflected by insect)
F'' = (Vo + Vr)F' / Vo
F'' = (340 + 4.70) x 61.45kHz / 340 .. .. .. ►F'' = answer 62.30 kHz

To determine the intensity level when both people speak at once, we need to use the concept of sound intensity and superposition.

1. First, let's understand the concept of sound intensity. Sound intensity is a measure of the amount of sound energy passing through a given area per unit of time. It is usually measured in decibels (dB).

2. According to your question, when one person speaks alone, the intensity level is 70 dB. This provides us with a reference point.

3. When multiple sound sources overlap or superpose, we need to use the principle of superposition to calculate the combined intensity level. The principle states that when waves combine, the displacement at any point is equal to the sum of the individual displacements at that point.

4. Since there are five people speaking simultaneously, each with an intensity level of 70 dB, the combined intensity level depends on whether the sound waves interfere constructively or destructively.

5. In this case, assuming that the sound waves interfere constructively, we can add up the intensities of each person speaking.

6. To calculate the combined intensity level, we use the formula for adding decibels on the intensity scale:

I_total = 10 * log10 (10^(I1/10) + 10^(I2/10) + ... + 10^(In/10))

Where I_total is the total intensity level and I1, I2, ..., In are the individual intensity levels.

7. Substituting the given intensity level of 70 dB into the formula:

I_total = 10 * log10 (10^(70/10) + 10^(70/10) + 10^(70/10) + 10^(70/10) + 10^(70/10))

8. Calculating the above expression:

I_total = 10 * log10 (10^7 + 10^7 + 10^7 + 10^7 + 10^7)
= 10 * log10 (5 * 10^7)
= 10 * (7 + log10 (5))
≈ 10 * (7 + 0.699)
≈ 10 * 7.699
≈ 76.99 dB

Therefore, when all five people speak simultaneously, the intensity level is approximately 76.99 dB.