A radio has a speaker that is emitting sound with a power of 50 W that is emitte

Question

A radio has a speaker that is emitting sound with a power of 50 W that is emitted in all directions equally. The radio is tuned to a frequency of 101.7 MHz. 1. (a) What is the wavelength of the signal that's received by the radio? (2 marks) (b) What is the sound intensity level in dB at 100 m from the radio speaker, assuming that the sound wave propagates with no loss? Identify at least one reason why the sound will lose energy while propagating and thus be quieter than this. (5 marks) (c) Explain why the sound intensity (in Wm2) at 200 m from the radio is four times lower than at 100 m, again assuming no loss. (2 marks)

Explanation / Answer

(a) Speed of radio waves, v = speed of light = 3.0 x 10^8 m/s

frequency, f = 101.7 MHz = 101.7 x 10^6 Hz

So, wavelength of the wave, lemda = v / f = (3.0 x 10^8) / (101.7 x 10^6) = 2.95 m

(b) Sound intensity at 100 m from the speaker, I = P / 4*pi*r^2 = 50 / (4*3.141*100^2) = 3.98 x 10^-4 W/m^2

(c) From above we see that Intensity, I is proportional to 1/r^2

take, r1 = 200 m and P1 as intensity

r2 = 100 m and P2 as intensity

so, P1 / P2 = r2^2 / r1^2 = 100^2 / 200^2 = 1/4

=> P1 = P2 / 4

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