1) A 5 m long pipe with one open and closed end is 30cm in diameter and has a 25

Question

1) A 5 m long pipe with one open and closed end is 30cm in diameter and has a 25 g string tied across its open end.  The fifth harmonic resonance (the third allowed) in the pipe's air column is induced which, in turn, excites the string to also vibrate.

To what tension (N) must the string be tuned so that it will also vibrate in its 5th harmonic?

2)A transverse wave travels alonga stretched string at a speed of 1.25 m/s. The string's linear density is 2.75 g/cm.At the string's x=10.0 cm position the vertical displacement of the string varies with time according to:

y(t)=0.25 cos (3.56 - 7.54 t)  (where y is in meters and t is in seconds)

WHAT IS THE WAVE'S VERTICAL DISPLACEMENT (IN m) AT x=81 cm and t= 3.5s?

Explanation / Answer

, in case of closed organ pipe fifth harmonic 9L/4 = 5m
So wavelength = L = 20/9 m
Hence frequency = c/L = 330*9/20 Hz
In case of string frequency = 1/2l ./ T/m
l is given as 0.3 m. Linear density of the string is needed. Then knowing frequency and all other data we can find required tension in the string.

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