Question

When one violin is playing at 440Hz, we expect a 80dB tone as heard in the audience. Suppose we have 32 identical violins playing now. What sound level do we expect to hear now?

Answer 1

Hi buddy!

Let me explain how to go about with this question!

Sound intensity level of one violin is given by the following equation

L_I(1) = 10 log( I₁ / I₀ ).

where I₁ is the intensity of one violin

Now the intensity of (suppose 4) violins can be taken as I_total = 4 I₁

now making use of a property of logarithms, log(A x B) = log A + log B, So the total sound intensity level is

L_I (total) = 10 log( 4 ) + 10 log( I₁ / I₀ ) = eqn 1

Here in the question, Sound intensity level of one violin is already given to be 80 db.

So this gives 10 log( i₁ / I₀) = 80 db ( From eqn 1)

so what is left to do is add 10 log (32) to 80 decibels to find he overall sound intensity level

10 log(32) = 15.05

Hence total sound intensity level is (15.05 + 80) = 95.05 db is the required solution

If this helped you please do leave a rating :)