Classifying standing waves and their frequencies

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SUMMARY

The discussion centers on the calculation of the frequency of a standing wave on a 40-cm long string, with one end clamped and the other free. The wave speed is given as 320 cm/s. The correct frequency for the fundamental mode is determined using the formula f = v/2L, where L is the length of the string. The correct calculation yields a frequency of 2 Hz, as the wavelength for the fundamental mode is equal to 4L, not 2L.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with standing waves
  • Knowledge of the wave speed formula
  • Basic algebra for solving equations
NEXT STEPS
  • Study the properties of standing waves in strings
  • Learn about the relationship between wave speed, frequency, and wavelength
  • Explore the concept of harmonics in vibrating strings
  • Investigate the differences between clamped and free boundary conditions
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators looking to clarify concepts related to standing waves and their frequencies.

Dalip Saini
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Homework Statement


40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is[/B]


  • A

    16 Hz


  • B

    8 Hz


  • C

    32 Hz
  • correct-icon.png


    D

    2 Hz
  • wrong-icon.png

    E
    4 Hz

Homework Equations


f = v/2L
because its fundamental

The Attempt at a Solution


I thought all one had to do was (320)/2(40) = 4Hz, but the answer is 2Hz. I don't understand why
 
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Dalip Saini said:

Homework Statement


40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is[/B]


  • A

    16 Hz


  • B

    8 Hz


  • C

    32 Hz
  • correct-icon.png


    D

    2 Hz
  • wrong-icon.png

    E
    4 Hz

Homework Equations


f = v/2L
because its fundamental

The Attempt at a Solution


I thought all one had to do was (320)/2(40) = 4Hz, but the answer is 2Hz. I don't understand why

The wavelength is not 2L.
 

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