You are playing a note that has a fundamental frequency of 440.00 Hz on a guitar string of length 59.1 cm. At the same time, your friend plays a fundamental note on an open organ pipe, and 4.0 beats per seconds are heard. The mass per unit length of the string is 1.93 g/m. Assume the velocity of sound is 343 m/s.

Question

You are playing a note that has a fundamental frequency of 440.00 Hz on a guitar string of length 59.1 cm. At the same time, your friend plays a fundamental note on an open organ pipe, and 4.0 beats per seconds are heard. The mass per unit length of the string is 1.93 g/m. Assume the velocity of sound is 343 m/s.
 
a) When the guitar string is tightened, the beat frequency decreases. Find the original tension in the string.

b)What is the length of the organ pipe?

bobpursley · Answer

a. well, beats are result of either a freq of 440+-4, but it is low, so f=436hz

you know half wavelength = 59.1cm
you know mass per length. You do not know wave velocity on the string.

Use http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html
solve for wave velocity first:
wavevelocity=2*length*frequency

b. Pipe organ, open pipe, lambda=2*length

you know frequency 440hz, solve for wavlength, lambda=speedsoundinAir/freq

now knowing wavelength, solve for length (lambda/2)