# Sound Pressure Level Formula

Last Updated : 04 Feb, 2024

The change in static pressure of the material through which a sound wave travels is known as sound pressure. It is denoted by the symbol p. The sound pressure level is the ratio of the actual sound pressure to the reference level, which is the lowest intensity sound. Basically, it is the value of pressure asserted by the sound waves while travelling in a medium of transmission.

Formula

It calculates the logarithmic ratio of the rms value of the sound pressure to the sound’s reference value using a factor of 20 log10. Its unit of measurement is the same as that of sound, that is, decibels (dB). It is denoted by the symbol Lp.

Lp = 20 log10(P / Pr)

where,

P is the actual root mean square sound pressure,

Pr is the sound pressure taken for reference.

The value of Pr is 20 Î¼P if the medium in which sound wave is travelling is air. For media other than air, its value decreases to 1 Î¼P.

### Sample Problems

Problem 1. Find the sound pressure level for a wave travelling in the air if the actual pressure value is 10 Î¼Pa.

Solution:

We have,

P = 10 and Pr = 20

Using the formula we have,

Lp = 20 log10(P / Pr)

= 20 log10 (10 / 20)

= -6.02 dB

Problem 2. Find the sound pressure level for a wave travelling in the air if the actual pressure value is 50 Î¼Pa.

Solution:

We have,

P = 50 and Pr = 20

Using the formula we have,

Lp = 20 log10(P / Pr)

= 20 log10 (50 / 20)

= 7.95 dB

Problem 3. Find the sound pressure level for a wave travelling in the air if the actual pressure value is 80 Î¼Pa.

Solution:

We have,

P = 80 and Pr = 20

Using the formula we have,

Lp = 20 log10(P / Pr)

= 20 log10 (80 / 20)

= 12.04 dB

Problem 4. Find the sound pressure level for a wave travelling in helium gas if the actual pressure value is 25 Î¼Pa.

Solution:

We have,

P = 25 and Pr = 1

Using the formula we have,

Lp = 20 log10(P / Pr)

= 20 log10 (25 / 1)

= 27.95 dB

Problem 5. Find the sound pressure level for a wave travelling in helium gas if the actual pressure value is 45 Î¼Pa.

Solution:

We have,

P = 25 and Pr = 1

Using the formula we have,

Lp = 20 log10(P / Pr)

= 20 log10 (25 / 1)

= 33.06 dB

Problem 6. Find the actual pressure for a wave travelling in the air if the SPL is 9.82 dB.

Solution:

We have,

Lp = 9.82 and Pr = 20

Using the formula we have,

Lp = 20 log10(P / Pr)

=> 9.82 = 20 log10 (P / 20)

=> P = 62 Î¼Pa

Problem 7. Find the actual pressure for a wave travelling in the air if the SPL is 11.23 dB.

Solution:

We have,

Lp = 11.23 and Pr = 20

Using the formula we have,

Lp = 20 log10(P / Pr)

=> 11.23 = 20 log10 (P / 20)

=> P = 73 Î¼Pa