# 12.1 Four waves, each with intensity 50 dB, interfere constructively. What is the intensity of the combined waves, in dB?

12.1
Four waves, each with intensity 50 dB, interfere constructively. What is the intensity of the combined waves, in dB?
12.2
A steel wire has density ρ=7800kg/m^3, radius 0.80 mm, and length 90.0 cm. A constant tension of 2.50 x 10^3 N is applied to the wire, and both ends are fixed.
(a)
What is the fundamental frequency of the wire?
(b)
Where should you pluck the wire to achieve the 5th harmonic, and what is its frequency?
(c)
What length of pipe closed at one end would have the same fundamental frequency as the wire in at (a)? Assume the speed of sound is 344 m/s.
12.3
(a) In which of these scenarios do you hear a higher pitched sound? Explain.
(i) A train with its horn sounding is stationary and you move directly towards it with a speed v0.
(ii) You stationary and the same train is sounding its horn as it moves directly towards you at speed v0.
(b) What is the difference in pitch between the above two scenarios if v0 =30 m/s, the frequency of the train horn is 800 Hz and the air temperature is 0°C (vsound = 332 m/s)?
(c) What is the difference in pitch in (b) if (hypothetically) v0 is one-third the speed of sound?
12.4 Two speakers are driven by the same amplifier and emit sinusoidal waves in phase. The speakers are on the x axis a distance d = 1.90 m apart. The frequency of the sound waves produced by the loudspeakers is 165Hz. For a point on the x axis between the two speakers, at what values of x will (a) destructive interference occur, and b)
constructive interference occur?
(c) Can destructive or constructive interference occur at a point on the x axis to the right of both speakers or to the left of both speakers? Explain. [Assume the temperature is 86 F (30 C) and the speed of sound is 350 m/s.]

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