Find New Frequency When Length AND Diameter Is Decreased?

In summary, the question asks for the new frequency of a string under tension when its length is decreased to 40cm, diameter decreased to 0.50mm and tension increased to 100 N. The wave speed, wavelength and frequency are all affected by these changes, and can be calculated using the equations v=fλ, f1/f2 = L2/L1, f1/f2 = Square Root F1/ Square Root F2, and f1/f2 = d2/d1. By combining these equations, the new frequency can be determined.
  • #1
justinh8
44
0

Homework Statement


Hi, i need some help with this question,
A string of length 60cm and diameter 0.80 mm is under tension 64 N. When plucked, it emits a frequency of 660Hz. What is the new frequency if the length is decreased to 40cm, the diameter decreased to 0.50mm and the tension increased to 100 N? Please explain, Thanks!


Homework Equations


f1/f2 = L2/L1, f1/f2 = Square Root F1/ Square Root F2, f1/f2 = d2/d1


The Attempt at a Solution


I can do it when one of the variables are decreased but i have no idea where to start when 3 variables are changing.
 
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  • #2
The wave speed depends on the tension, the wavelength depends on the length of the string. Do each separately and combine to get frequency. The equation you are missing is v=fλ.
 

FAQ: Find New Frequency When Length AND Diameter Is Decreased?

What is the relationship between frequency, length, and diameter?

The frequency of an object is inversely proportional to its length and directly proportional to its diameter. This means that as the length of an object decreases, its frequency increases, and as the diameter increases, its frequency also increases.

How do you calculate the new frequency when both length and diameter are decreased?

To calculate the new frequency when both length and diameter are decreased, you can use the formula f2 = f1 x (l2/l1) x (d2/d1), where f1 is the original frequency, l1 is the original length, d1 is the original diameter, f2 is the new frequency, l2 is the new length, and d2 is the new diameter.

Can the frequency increase indefinitely as the length and diameter decrease?

No, the frequency cannot increase indefinitely. There is a limit to how small the length and diameter can be before the object is no longer able to vibrate at a higher frequency. This limit is determined by the material properties and structural integrity of the object.

What factors affect the frequency when both length and diameter are decreased?

The main factors that affect the frequency when both length and diameter are decreased are the material properties of the object, the structural integrity of the object, and the mode of vibration (i.e. bending, torsion, etc.). Additionally, any external forces or damping effects can also impact the frequency.

Why is it important to consider both length and diameter when finding the new frequency?

Both length and diameter have a significant impact on the frequency of an object. Neglecting one of these factors can lead to inaccurate calculations and predictions. It is important to consider both length and diameter in order to get a complete understanding of the relationship between frequency, length, and diameter.

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