Question

Three sources of sound ${S_1}$ ,${S_2}$ and ${S_3}$ of equal intensity are placed in a straight line with ${S_1}{S_2} = {S_2}{S_1}$. At a point P, far from the sources, the waves coming from ${S_2}$is ${120^ \circ }$ a head in phase of that from${S_1}$. Also, the wave coming from ${S_3}$is ${120^ \circ }$ ahead of that from ${S_2}$ . What would be the resultant intensity of sound at P?

Answer 1

Hint: Intensity of sound, the energy carried by sound waves per unit area in a direction perpendicular to the area. SI unit of intensity, which includes sound intensity, is the watt per square meter.

Complete step by step solution:
 According to the questions we have,
Three source having equal intensity${S_1}{S_2} = {S_2}{S_3}$,

which means amplitude of sound source are also equal,
Let us consider that amplitude of ${S_1}$ $ = {A_1}$,
Amplitude of ${S_2}$ $ = {A_2}$ and Amplitude of ${S_3}$ $ = {A_3}$ Fig.(1)
Whereas, Amplitude of all sources are ${A_1} = {A_2} = {A_3}$
From Fig (1) wave coming from ${S_2}$$ = {120^ \circ }$ ahead of ${S_1}$ and Wave coming from ${S_3}$$ = {120^ \circ }$ ahead of ${S_2}$As we know, for sound the intensity $I$ is directly proportional to the square of the amplitude of longitudinal waves, we can written as,
$I \propto {A^2}$
I stand for Intensity of Sound wave
A is for Amplitude of Sound wave

Hence, the resultant intensity of sound at point P is zero by vector method.

Note:The intensity of a sound wave is a sum or combination of its density and rate of energy transfer moreover; Sound waves with large amplitudes are called low. Sound waves with small amplitudes are called soft. Remember, sound level and sound intensity both are different.