Question

Problem 54

Answer 1

Given information

Given values:

The length of the string,

The string's mass,

    

The string's tension,

 

 

Between the bridge and the support post, there is a distance of,

 

Formula used:

The length of the string determines the speed of the waves.

 

 

 

When both ends of a string are fixed, the resonant frequencies are given by

 

 

 

where, is the length of the actual vibrating section.

Step-by-step explanation

Step 1.

In the fundamental mode of vibration, if an inextensible string is put between two rigid supports, a full-wave (half-wavelength) loop forms on the string. When a whole wave is formed on a string, that is, when the length of the string between the supports equals the '' the frequency of the vibration is generally referred to as the second harmonic or the first overtone. The frequency of vibration is described as follows:

   

where:

 

The harmonic number is .

The wave speed is denoted by .

The distance between the fixed points is denoted by the letter  .

The wavelength of the wave is denoted by the letter .