Question

calculate the total sound pressure level caused by a combination of sounds with the following SPL,s (a) 25db and 39db (b)60db+60db+60db

Answer 1

QUESTION:

Calculate the total sound pressure level caused by a combination of sounds with the following SPL,s (a) 25db and 39db (b)60db+60db+60db

SOLUTION:

The sum level of sound pressures of non-coherent sound waves is

$$\mathrm {L} _ {\text {t o t a l}} = 1 0 \lg \left(\frac {\mathrm {p} _ {1} ^ {2} + \mathrm {p} _ {2} ^ {2} + \dots \mathrm {p} _ {\mathrm {n}} ^ {2}}{\mathrm {p} _ {\text {r e f}} ^ {2}}\right) = 1 0 \lg \left(\left(\frac {\mathrm {p} _ {1}}{\mathrm {p} _ {\text {r e f}}}\right) ^ {2} + \left(\frac {\mathrm {p} _ {2}}{\mathrm {p} _ {\text {r e f}}}\right) ^ {2} + \dots + \left(\frac {\mathrm {p} _ {\mathrm {n}}}{\mathrm {p} _ {\text {r e f}}}\right) ^ {2}\right)$$ $$\text {A s} \mathrm {L} _ {\mathrm {i}} = 1 0 \lg \left(\frac {\mathrm {p} _ {\mathrm {i}}}{\mathrm {p} _ {\text {r e f}}}\right) ^ {2} \Rightarrow \left(\frac {\mathrm {p} _ {\mathrm {i}}}{\mathrm {p} _ {\text {r e f}}}\right) ^ {2} = 1 0 ^ {\frac {\mathrm {L} _ {\mathrm {i}}}{1 0}}, \text {h e n c e}$$ $$\mathrm {L} _ {\text {t o t a l}} = 1 0 \lg \left(1 0 ^ {\frac {\mathrm {L} _ {\mathrm {i}}}{1 0}} + 1 0 ^ {\frac {\mathrm {L} _ {2}}{1 0}} + \dots + 1 0 ^ {\frac {\mathrm {L} _ {\mathrm {n}}}{1 0}}\right)$$

a) $\mathrm{L}_{\text {total }} = 10 \lg \left(10^{\frac{\mathrm{L}_i}{10}} + 10^{\frac{\mathrm{L}_2}{10}}\right) = 10 \lg \left(10^{\frac{25}{10}} + 10^{\frac{39}{10}}\right) = 39.17$ dB

b) $\mathrm{L}_{\text {total }} = 10 \lg \left(10^{\frac{\mathrm{L}_i}{10}} + 10^{\frac{\mathrm{L}_2}{10}} + 10^{\frac{\mathrm{L}_3}{10}}\right) = 10 \lg \left(10^{\frac{60}{10}} + 10^{\frac{60}{10}} + 10^{\frac{60}{10}}\right) = 10 \lg \left(3 \cdot 10^{\frac{60}{10}}\right) = 64.77$ dB

ANSWER:

a) 39.17 dB

b) 64.77 dB