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What is maximum possible wavelength of standing waves in 1m long string if it is fixed at both ends

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To find the maximum possible wavelength of standing waves in a 1-meter long string that is fixed at both ends, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Setup**: The string is fixed at both ends, which means that the ends of the string are nodes (points of no displacement). 2. **Identifying the Wavelength**: ...
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Standing Wave Vibrations of string fixed at both ends

You have a microwave generator that can produce microwaves at any frequency between 1 GHz and I0 GHz . The microwave radiation enters a 10 cm long cylinder with reflective cnd caps, as shown in the figure. What frequency of the microwave generator (in GHz ) will produce the lowest-order' standing wave with an antinode (maximum) in the center of the cavity? Note that with reflectors at both ends, the electromagnetic standing wave acts just like the standing wave on a string that is tied at both ends. Take velocity of waves as 3 xx 10^(8) m / s. '(##CEN_KSR_PHY_JEE_C17_E01_002_Q01##)'

Knowledge Check

  • Estimation of frequency of a wave forming a standing wave represented by y = A sin kx cos t can be done if the speed and wavelength are known using speed = "Frequency" xx "wavelength" . Speed of motion depends on the medium properties namely tension in string and mass per unit length of string . A string may vibrate with different frequencies . The corresponding wavelength should be related to the length of the string by a whole number for a string fixed at both ends . Answer the following questions: Speed of a wave in a string forming a stationary wave does not depend on

    A
    Tension
    B
    Mass of wire for a given length
    C
    Length of the wire for a given mass
    D
    Harmonics of string
  • lambda is maximum wavelength of a transverse wave that travels along a stretched wire whose two ends are fixed. The length of that wire is

    A
    `2lambda`
    B
    `lambda`
    C
    `lambda//2`
    D
    `3lambda//2`
  • One end of a 2.4 - m string is held fixed and the other end is attached to a weightless ring that can slide along a frictionless rod as shown in Fig. 7.86. The three longest possible wavelength for standing waves in this string are respectively

    A
    `4.8 m , 1.6 m and 0.96 m`
    B
    `9.6 m , 3.2 m and 1.92 m`
    C
    `2.4 m , 0.8 m and 0.48 m`
    D
    `1.2 m , 0.4 m and 0.24 m`
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    Standing Waves In A Strings Fixed At Both Ends

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    Estimation of frequency of a wave forming a standing wave represented by y = A sin kx cos t can be done if the speed and wavelength are known using speed = "Frequency" xx "wavelength" . Speed of motion depends on the medium properties namely tension in string and mass per unit length of string . A string may vibrate with different frequencies . The corresponding wavelength should be related to the length of the string by a whole number for a string fixed at both ends . Answer the following questions: A string fixed at both ends having a third overtone frequency of 200 Hz while carrying a wave at a speed of 30 ms^(-1) has a length of

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