Possible Frequencies of Tuning Fork with Fixed Wire: 5.20 Hz Beat Frequency

[DDS]

A 0.0145 kg, 1.92 m long wire is fixed at both ends and vibrates in its simplest mode under a tension of 193 N. When a tuning fork is placed near the wire, a beat frequency of 5.20 Hz is heard. What are the possible frequencies of the tuning fork?

B)What should the tension in the wire be if the beats are to disappear?

for part A i have calcuated

u=7.55e-3 and velocity along the string which is v=159 m/s

what i am thinking of doing is the following:

i know my beat freq. is 5.20 Hz. I also know that

Freq.b = Delta w/2pi

i am thinking of rearanging to find w and then pluging everything into:

F= 1/2pi * srt w

that may give me one frequency of the tunning frok and then from here i take the frequency from my answer and then minus my beat frequency from it giving me my other frequency.

Is this what i have to do??

and for B) I am not really sure how to approach it any hints?

 

[DDS]

is this the correct method or am i doing something wrong?

 

[DDS]

can anyone out there help me please

 

[OlderDan]

A 0.0145 kg, 1.92 m long wire is fixed at both ends and vibrates in its simplest mode under a tension of 193 N. When a tuning fork is placed near the wire, a beat frequency of 5.20 Hz is heard. What are the possible frequencies of the tuning fork?

B)What should the tension in the wire be if the beats are to disappear?

for part A i have calcuated

u=7.55e-3 and velocity along the string which is v=159 m/s

what i am thinking of doing is the following:

i know my beat freq. is 5.20 Hz. I also know that

Freq.b = Delta w/2pi

i am thinking of rearanging to find w and then pluging everything into:

F= 1/2pi * srt w

that may give me one frequency of the tunning frok and then from here i take the frequency from my answer and then minus my beat frequency from it giving me my other frequency.

Is this what i have to do??

and for B) I am not really sure how to approach it any hints?

Your velocity round off could be better. Where is the frequency of vibration of the string? You need it as a reference point to combine with the beat frequency to find the tuning fork frequency.

The last part is simply matching the frequency of the string to the frequency of the tuning fork. Since there are two possible fork frequencies, there will be two possible tensions, one looser and one tighter than the starting tension.

Beats can be used to help tune a stringed instrument like a guitar to itself. It is often done by forcing it to vibrate in a harmonic mode by simply touching the string in the right places to create vibration nodes, then playing another string to listen for any beats.

 

[DDS]

"Where is the frequency of vibration of the string?"

I am not sure, could you elabortae further?

 

[DDS]

got it thanks for the help