An organ pipe is 1.90 meters long. It can be played with both ends open, which s

Question

An organ pipe is 1.90 meters long. It can be played with both ends open, which supports standing waves that have antinodes at each end. It can also be played with only one end open, which supports standing waves that have an antinode at the open end, and a node at the closed end. a) For the pipe that's open at both ends, find the wavelengths of two largest possible waves whose antinodes can fit the pipe. First (largest) Wavelength: Second Wavelength: b) For the pipe that's closed at one end and open at the other, find the wavelengths of two largest possible waves whose antinodes can fit the pipe. First Wavelength: Second Wavelength: c) The speed of sound is 343 m/s. For each of the wavelengths, find the corresponding frequencies. OPEN First frequency: Second frequency: CLOSED First frequency: Second frequency

Explanation / Answer

Given that

length L=1.9 m

basing on the concept of oscillations and waves

now we find the possible wavelengths of open pipe

frst wavelength =2L=2*1.9=3.8 m

second wavelength =2L/2=2*1.9/2=1.9 m

now we find the possible wavelengths of closed pipe

first wave length =4L=4*1.9=7.6 m

second wavelength =4L/2=2*1.9=3.8 m

now we find the frequencies of both pipes

open pipe :-

first frequency f1=343/3.8=90.3 Hz

second frequency f2=343/1.9=180.53 Hz

closed pipe :-

first frequency f1=343/7.6=45.1 Hz

second frequency f2=343/3.8=90.3 Hz

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