Aguitar string is 95 cm long and has a mass of 3.3 g. the length l from the bridge to the support post is 66 cm, and the string is under a tension of 580 n. what is the frequency of the fundamental tone?

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

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