Question

#1 If the fundamental frequency of an 76 cm long guitar string is 460 Hz, what is the speed of the traveling waves?

#2: You have an organ pipe that resonates at frequencies of 800, 1120, and 1440 Hz but nothing between these. It may resonate at lower and higher frequencies as well. What is the fundamental frequency for this pipe?

Answer 1

1. For a streched string as in a guitar,

Fundamental frequency is given by:

where v is the speed of travelling wave and L ia the length of the streched string.

Substitute the given values of fundamental frequency and Length in above equation:

2. Organ pipe resonates at following frequencies:

800 Hz, 1120 Hz, 1440 Hz

Assuming this is a closed end organ pipe, the resonating frequencies are given by:

f₀=v/4L

f₁=3v/4L

f₂=5v/4L

and so on

so in general it resonates at f=(2n+1)v/4L

Subtracting 2 consecutive resonant frequencies:

and

so in general,

where n'=n+1

from this we can see that fundamental frequency is 1/2 the difference between consecutive resonant frequencies:

Thus we find the diffeence between given resonant frequencies and divide it by 2 to get fundamental frequency:

or,

fundamental frequency: