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## Homework Statement

An organ pipe is 2.5 m long and has a cross-sectional area of 30 cm^2. The pipe is open at one end and closed at the other. The equation of the displacement s of an air molecule from its equilibrium position is

s=(0.5 cm) sin (pi x) cos (900pi t) where x is the distance from the closed end in meters, and t is the time in seconds starting with a time when its displacements are maximum.

(i) What is the average speed of an air molecule at a displacement antinode?

(ii) What would be the wave speed of a sound wave that travelled down an organ pipe of infinite length containing air at the same temperature and pressure as in the pipe containing the stationary wave described above?

(iii) What is the lowest possible frequency of a stationary wave in the organ pipe described above?

(iv) Once you know all constant characteristics of a given gas, which of the following variable properties, by itself, determines the speed of sound waves in that gas: pressure, temperature, volume, density? Justify your answer.

## Homework Equations

k=2 π/ λ

w= 2 π f

v=λf

2A sin kx is the maximum antinode where x = (2k+1) (λ/4)

## The Attempt at a Solution

For i) I think at the displacement antinode, the speed of a particle will be 0 because it's the maximum displacement or it could be the greatest average vertical speed?

ii) Not sure for when it says infinite length? We can find λ and f and use v=fλ?

iii) f=v/L? Not sure when it says described above whether its referring to part i or ii?

c) Either pressure or density-not sure

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