A. If two firecrackers produce a sound level of 70dB when fired simultaneously a

Question

A. If two firecrackers produce a sound level of 70dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB's.]
B=....dB

B. An organ pipe is 120cm long.
1. What are the fundamental and first three audible overtones if the pipe is closed at one end?
Ffund f1,f2,f3,.... Hz

2. What are the fundamental and first three audible overtones if the pipe is open at both ends?
Ffund f1,f2,f3,.... Hz


C. A tight guitar string has a frequency of 540 Hz as its third harmonic.

What will be its fundamental frequency if it is fingered at a length of only 80% of its original length?

f....Hz

Explanation / Answer

Sound intensity level in dB is defined as:
L = 10·log10( I/I0 )
where I0 is he threshold of hearing

Let the two firecracker have intensity I and Level, then the intensity of a single firecracker is I/2. So its sound level is:
L' = 10·log10( (I/2)/I0 )

Since log(a/b) = log(a) - log(b) you can rewrite:
L' = 10·log10( I/I0 ) - 10·log10( 2 )
    = L - 10·log10( 2 )
    = 70 dB - 3 dB
   = 67 dB ** please post each question separately...

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