A tube 1.2 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.3 m long and has a m

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A tube 1.2 m long is closed at one end. A stretched wire is
placed near the open end. The wire is 0.3 m long and has a mass of
5 g. It is fixed at both ends and oscillates in its fundamental
mode. By resonance, it sets the air in the tube into oscillation at
fourth harmonic frequency. Determine that frequency f and the
tension 𝜏 in the wire. Given that the speed of sound in air is 343
m/s. (10 marks)
(b) A stationary detector measures the frequency of a sound
source that first moves at constant velocity 𝑣𝑠 directly towards
the detector and then directly away from it. The emitted frequency
is 𝑓. During the approach the detected frequency is 𝑓′𝑎𝑝𝑝 and
during the recession it is 𝑓′𝑟𝑒𝑐. If 𝑓 ′ 𝑎𝑝𝑝 − 𝑓 ′ 𝑟𝑒𝑐 = 2𝑓,
calculate the speed of the source 𝑣𝑠 . Given that the speed of
sound in air is 343 m/s.