Answer:
The frequency of the fundamental tone is 309.56 hz
Explanation:
The frequency of the fundamental tone is given by the following equation:
Where is the frequency of the fundamental tone, v is the velocity of the wave on the string and L is the length of the string that is vibrating.
From the question we know that L is 66 cm.
On the other hand, the velocity can be calculate as:
Where T is the tension, is the total mass of the string and is the total length of the string
From the question we know that T is 580N, is 3.3g and is 95 cm.
For not have problems with units, T needs to be in Newtons, L and needs to be in meters and m need to be in Kg. So the transform values are
L=0.66m
m=0.0033 Kg
T=580N
Replacing on the equation of velocity we get:
Now with the value of the velocity of the wave. we can calculate the value of the frequency of the fundamental tone as:
So, The frequency of the fundamental tone is 309.56 hz