QUIZ 13

1. A stereo tape recorder is said to have a signal-to-noise ratio of 58dB. What is the ratio of intensities of the signal and the background noise?

Solution. We find the ratio from

                   b = 10log₁₀(I_signal/I_noise);

                   58dB = 10log₁₀(I_signal/I_noise), which gives I_signal/I_noise = 6.3 x 10⁵.

2.  Two loudspeakers are 1.50m apart. A person stands 5.00m from one speaker. How far must this person be from the second speaker in order to detect destructive interference when the speakers emit an 1150-Hz sound? Assume the temperature is 20˚C.

Solution. The wavelength of this sound is

                l = v/f = (343m/s)/(1150Hz) = 0.30m.

For destructive interference to occur, the person must be one-half wavelength farther from one loudspeaker than from the other, or 0.30m/2 = 0.15m. Thus the person must be 5.00m + 0.15m = 5.15m (or 5.00m- 0.15m = 4.85m) from the second speaker.