# Sound Pressure Level Formula

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 log_{10}. Its unit of measurement is the same as that of sound, that is, decibels (dB). It is denoted by the symbol L_{p}.

L_{p}= 20 log_{10}(P_{ }/ P_{r})where,

P is the actual root mean square sound pressure,

P

_{r }is the sound pressure taken for reference.The value of P

_{r }is 20 μP if the medium in which sound wave is travelling is air. For media other than air, its value decreases to 1 μP.

**Sample Problems**

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

**Solution:**

We have,

P = 10 and P

_{r}= 20Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})= 20 log

_{10}(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 μPa.**

**Solution:**

We have,

P = 50 and P

_{r}= 20Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})= 20 log

_{10}(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 μPa.**

**Solution:**

We have,

P = 80 and P

_{r}= 20Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})= 20 log

_{10}(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 μPa.**

**Solution:**

We have,

P = 25 and P

_{r}= 1Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})= 20 log

_{10}(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 μPa.**

**Solution:**

We have,

P = 25 and P

_{r}= 1Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})= 20 log

_{10}(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,

L

_{p}= 9.82 and P_{r}= 20Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})=> 9.82 = 20 log

_{10}(P / 20)=> P = 62 μPa

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

**Solution:**

We have,

L

_{p}= 11.23 and P_{r}= 20Using the formula we have,

L

_{p}= 20 log_{10}(P / P_{r})=> 11.23 = 20 log

_{10}(P / 20)=> P = 73 μPa