An engine whose sparkplugs fire 120 times a second generates noise at 120 Hz. The sound level can be reduced by fitting the engine with an exhaust resonator that cancels this primary "note." The resonator is an open-closed tube, with the open end connected to the exhaust system. Sound enters the tube, reflects from the closed end, and re-enters the exhaust system exactly out of phase with the incoming sound. How long must the tube be? Assume a sound speed of 360 m/s in the warm exhaust gases.

Question

Physics

Madeleine Anderson

19 July, 07:58

An engine whose sparkplugs fire 120 times a second generates noise at 120 Hz. The sound level can be reduced by fitting the engine with an exhaust resonator that cancels this primary "note." The resonator is an open-closed tube, with the open end connected to the exhaust system. Sound enters the tube, reflects from the closed end, and re-enters the exhaust system exactly out of phase with the incoming sound. How long must the tube be? Assume a sound speed of 360 m/s in the warm exhaust gases.

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Carlos · Answer 1

Answer: length of tube = 0.95m

Explanation: frequency of sound wave in resonator = 120Hz.

Resonator is an open tube hence the relationship between it length and wavelength of sound passing through it is given by the formulae below

L = λ/4

Where L = length of resonator and λ = wavelength of sound in resonator.

Hence λ = 4L.

But v = fλ where v = 360m/s, λ = 4L and f = 120Hz

We have that

360 = 120 * 4L

360 = 480 * L

L = 360 / 480

L = 0.95m