Question

Tom walks around S1 in a circular path. The two loud speakers S1 (0, 0) and S2 (0,10m) are driven by the same oscillator are identical with adjustable frequencies and power 300-watt each. Assume sound intensity does not decay due to the distance and it is Io=kA2(A is the amplitude of a sound wave). When Tom is at point P (10, 0), he receives a maximum intensity of sound.

(a) What are the frequencies of the two speakers?
(b) What is the sound intensity and sound level (in dB) at point P?

Answer 1

Part a)

`f = 82.8 Hz`

Part b)

`I_(max) = 0.95 Watt/m^2`

`L = 119.8 dB`

Step-by-step explanation:

Path difference of two sounds reaching at the position of Tom is given as

`\Delta L = L_1 - L_2`

here we know that

`L_1 = 10\sqrt2`

`L_2 = 10`

now we have

`\Delta L = 10\sqrt2 - 10`

so we know that path difference must be equal to wavelength for maximum intensity of sound

so we have

`\lambda = 10(\sqrt2 - 1)`

`\lambda = 4.14 m`

now frequency of sound is given as

`f = (v)/(\lambda)`

`f = (343)/(4.14)`

`f = 82.8 Hz`

Part b)

Intensity of source at position of Tom is given as

`I = (P)/(4\pi r^2)`

so we have

`I = (300)/(4\pi(10)^2)`

`I = 0.24`

now due to constructive interference the maximum intensity is given as

`I_(max) = 4I`

`I_(max) = 0.95 Watt/m^2`

now sound level is given as

`L = 10 Log(I)/(I_0)`

`L = 10 Log(0.95)/(10^(-12))`

`L = 119.8 dB`