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Fundamental frequency of a sonometer wire when its length or tension changes

This type of question, asked 3 times: 8 Apr 2023, 13 Apr 2023, 5 Apr 2024. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    8 Apr 2023

    112
    A guitar string of length 90 cm90\text{ }cm vibrates with a fundamental frequency of 120 Hz120\text{ }Hz. The length of the string producing a fundamental frequency of 180 Hz180\text{ }Hz will be____ cmcm.

  2. Question 2

    13 Apr 2023

    116
    In an experiment with sonometer when a mass of 180 g180\text{ }g is attached to the string, it vibrates with fundamental frequency of 30 Hz30\text{ }Hz. When a mass mm is attached, the string vibrates with fundamental frequency of 50 Hz50\text{ }Hz. The value of mm is ____\_\_\_\_ g.

  3. Question 3

    5 Apr 2024

    114
    A sonometer wire of resonating length 90 cm90\text{ }cm has a fundamental frequency of 400 Hz400\text{ }Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz600\text{ }Hz under same tension ____ cmcm.