The sound from a trumpet radiates uniformly in all directions in [math]20^{\circ} C[/math] air. At a distance of 5.00 m from the trumpet the sound intensity level is 52.0 dB. The frequency is 587 Hz. (a) What is the pressure amplitude at this distance? (b) What is the displacement amplitude? (c) At what distance is the sound intensity level 30.0 dB?

Part a)

Pressure amplitude is

Part b)

displacement amplitude is given as

Part c)

Distance at the other intensity is

Explanation:

Part a)

As we know that intensity of sound at 5 m distance is 52 dB

so we have

now we have

Now we know that speed of sound at 20 degree C is given as

Now we know the relation of intensity of wave and pressure amplitude as

Part b)

Now displacement amplitude with pressure amplitude is related as

now bulk modulus of air is given as

also we know that

now we have

so we have

Part c)

As we know that intensity is inversely depends on the square of the distance

so we will have