Take two sinusoids of 2 kHz, both with a phase of 0°. One has a peak level of 1.

Question

Take two sinusoids of 2 kHz, both with a phase of 0°. One has a peak level of 1.2 Pa while the other has a peak level of 0.7 Pa.

(a) What are the individual peak levels of the two sinusoids in dB SPL?

(b) What would be their peak level (in dB SPL) if added?

(c) If one had a phase of 180° while the other remained at 0°, what level would the sum of these two sinusoids be, in Pa and dB SPL?

I have seen the answer for this question on the site but I do not understand how to complete c), Detail on how to complete c) would be much appreciated!

Explanation / Answer

a) the individual peak levels of the two sinusoids:

for peak level of 1.2 Pa, dB = 20 log(p1/p0) = 95.6 dB SPL

for peak level of 0.7 Pa, dB = 20 log(p2/p0) = 90.9 dB SPL

b) When they added, peak level = 1.2+0.7 = 1.9 Pa = 99.6 dB SPL

c) when they are out of phase( = 180 degree), if they added, then peak level = 1.2 - 0.7 = 0.5 Pa = 88 dB SPL.

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