A standing wave pattern in an organ pipe. The length of the pipe is 1.10 m, its

Question

A standing wave pattern in an organ pipe. The length of the pipe is 1.10 m, its diameter is 1.2 cm. The speed of the sound wave in the pipe is 345.0 m/s. Show work please

a) what is in meters the wavelength of the oscillating wave?

b) what is in hertz the frequency of the oscillating wave?

A tuning fork of frequency 241Hz was approached to the pipe and beats were heard.

c) what is in hertz the beat frequency heard?

The tuning fork was removed but the pipe was kept oscillating at the frequency you calculated in part b.

d) What would be in Hz, the frequency perceived by a cyclist moving towards the organ at 7.0m/s?

e) what is in hertz the fundamental frequency of this pipe?

Explanation / Answer

A) total leength is lamda/2 + lamda/4 = L =1.1

(3/4)*lamda = 1.1

lamda = 1.1*4/3 = 1.46 m

B) v = lamda*f

frequency is f = v/lamda = 345/(1.46) = 235.22 Hz

C) beat frequency is 241-235 = 6 beats/s

D) f' = (V+VL)*f/V = (345+7)*235/345 = 240

E) we got ist overtone frequency = 3*fundamental frequency

fundamental frequency is 235/3 = 78.33 Hz

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