The intensity of a sound wave at a fixed distance from a spe

The intensity of a sound wave at a fixed distance from a speaker vibrating at 1.00 kHz is 0.500 W/m².

(a) Determine the intensity if the frequency is increased to 2.30 kHz while a constant displacement amplitude is maintained.
W/m²

(b) Calculate the intensity if the frequency is reduced to 0.250 kHz and the displacement amplitude is quadrupled.
W/m²

Solution

According to the given probelm,

As we know that

I f² if other factors are constant.
I A² if other factors are constant.

a) As f is changed by a factor 2.3, so the intensity I changes to

0.500* 2.3² = 2.645 W/m²

b) As f is changed by a factor 0.25 and A is changed by a factor 4, so the intensity I changes to

0.500*0.25² *4² = 0.500W/m² (i.e. no change).