Standing waves hanging in pulley problem

In summary, a standing wave hanging in pulley problem involves a string or rope being tied to a pulley and pulled taut, creating a standing wave pattern with nodes and antinodes that remain stationary in space. Standing waves form when two waves with the same frequency and amplitude interfere with each other, and the tension in the string affects the frequency of the standing wave. This concept has practical applications in musical instruments such as guitars and pianos.
  • #1
a077456
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In the calculation of the theoretical speed vtheo. = √(F_T/μ) (7), the mass associated with the length of the string hanging over the pulley was not taken into account. Suppose that the length of string hanging over the pulley is 20cm and that the hanging mass is 100 grams. What percentage error in the theoretical value of the wave velocity would result from ignoring the hanging string mass in this case?
 
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  • #2
What is [tex]\mu[/tex]? (check the dimension).
Why would you expect sound velocity to be dependent on length?
 

FAQ: Standing waves hanging in pulley problem

1. What is a standing wave hanging in pulley problem?

A standing wave hanging in pulley problem is a physics concept that involves a string or rope being tied to a pulley and then being pulled taut. The tension created in the string causes a standing wave pattern to form, with nodes and antinodes that remain stationary in space.

2. How do standing waves form in this type of problem?

Standing waves form when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. In the case of a standing wave hanging in pulley problem, this occurs when the string is pulled tight and the reflected wave from the pulley interferes with the original wave.

3. What is the significance of nodes and antinodes in this problem?

Nodes are points on the string where the amplitude of the wave is always zero, while antinodes are points where the amplitude is at its maximum. In a standing wave hanging in pulley problem, the nodes and antinodes remain stationary in space, creating a distinct pattern that can be observed.

4. How does the tension in the string affect the standing waves?

The tension in the string is directly related to the frequency of the standing wave. As the tension increases, the frequency of the standing wave also increases. This means that the distance between nodes and antinodes decreases, creating a higher frequency standing wave.

5. Can standing waves in a pulley problem be used for any practical applications?

Yes, standing waves in a pulley problem have practical applications in instruments such as stringed instruments like guitars and pianos. The standing wave patterns created by the tension in the strings produce distinct musical notes that can be manipulated to create different sounds and melodies.

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