Find Minimum Frequency to Establish Standing Wave on Wire

In summary, the student is trying to establish a standing wave on a wire clamped at both ends and with a wave speed of 587 m/s. They are unsure of the necessary frequency and have attempted to calculate it by dividing the wave speed by the wire's length. However, this is not the minimum frequency. The student is advised to consider the simple formula relating wave speed and frequency and to determine the longest wavelength for a standing wave on a 1.7m wire clamped at both ends.
  • #1
physicsya
1
0

Homework Statement


A student wants to establish a standing wave on a wire 1.7 m long clamped at both ends.
The wave speed is 587 m/s. What is the minimum frequency she should apply to set up standing waves?


Homework Equations


Not sure...need help here? :)


The Attempt at a Solution


I tried 587 / 1.7 which is 345. 294
 
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  • #2
Hi physicsya,

physicsya said:

Homework Statement


A student wants to establish a standing wave on a wire 1.7 m long clamped at both ends.
The wave speed is 587 m/s. What is the minimum frequency she should apply to set up standing waves?


Homework Equations


Not sure...need help here? :)

What simple formula has wave speed and frequency in it?

The Attempt at a Solution


I tried 587 / 1.7 which is 345. 294

This is close, in that you have found one of the frequencies of a standing wave. It's just not the minimum frequency.

For a string that is 1.7m long and clamped at both ends, what is the longest wavelength for a standing wave? (It is not 1.7m.)
 
  • #3
1 Hz but I'm not sure if this is correct.

I can provide a more detailed and accurate response to this question. First, we need to understand the concept of standing waves and how they are created. Standing waves are formed when two waves with the same frequency and amplitude, traveling in opposite directions, interfere with each other. In the case of a wire clamped at both ends, the standing wave is created when the incident wave reflects back and interferes with the original wave.

The standing wave on a wire is determined by its length, tension, and mass per unit length. In this scenario, the length of the wire is given as 1.7 m and the wave speed is 587 m/s. We can use the equation for the fundamental frequency of a standing wave on a wire, which is f = v/2L, where v is the wave speed and L is the length of the wire.

Substituting the given values, we get f = 587/2(1.7) = 172.65 Hz. This is the minimum frequency required to establish a standing wave on the wire. Any frequency higher than this will also create a standing wave, but it will have a higher number of nodes and antinodes.

It is important to note that the tension and mass per unit length of the wire also play a role in determining the frequency of the standing wave. If these values are changed, the minimum frequency required to establish a standing wave will also change.

In conclusion, the minimum frequency required to establish a standing wave on a wire 1.7 m long, clamped at both ends, with a wave speed of 587 m/s is 172.65 Hz. This can be calculated using the equation f = v/2L, where v is the wave speed and L is the length of the wire.
 

1. What is a standing wave?

A standing wave is a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in a wave pattern that appears to be standing still.

2. How is frequency related to standing waves on a wire?

The frequency of a standing wave on a wire is directly related to the length of the wire and the speed of the wave. The minimum frequency required to establish a standing wave on a wire is determined by the length of the wire and the speed of the wave.

3. What factors can affect the minimum frequency needed for a standing wave on a wire?

The length and thickness of the wire, as well as the tension and density of the material, can all affect the minimum frequency required for a standing wave on a wire. Additionally, the type of wave (transverse or longitudinal) and the boundary conditions of the wire can also play a role.

4. How can the minimum frequency for a standing wave on a wire be calculated?

The minimum frequency can be calculated using the formula f = n(v/2L), where f is the frequency, n is the number of nodes (points of no motion) on the wire, v is the speed of the wave, and L is the length of the wire. This formula is based on the fundamental mode of standing waves on a wire.

5. Can the minimum frequency for a standing wave on a wire be adjusted?

Yes, the minimum frequency can be adjusted by altering the length, thickness, tension, or material of the wire. By changing these factors, the speed of the wave and the number of nodes on the wire can be modified, which in turn affects the minimum frequency required for a standing wave.

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