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Converting between phase difference and path difference using wavelength = velocity / frequency

This type of question, asked 10 times: May 2021 S1, May 2022 S1, 2 May 2023 S1, 4 May 2023 S1, 4 May 2023 S2, 15 May 2023 S2, 19 Apr 2025 S2, 13 Apr 2026 S2, 13 May 2026 S1, 15 May 2026 S2. All 11 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    13
    A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60∘60^\circ out of phase?

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  2. Question 2

    May 2022 S1

    14
    In a medium, the phase difference between two particles separated by a distance xx is π5\frac{\pi}{5} rad. If the frequency of the oscillation of particles is 25 Hz and the velocity of propagation of the waves is 75 m/s, then the value of xx is

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  3. Question 3

    2 May 2023 S1

    34
    Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of 1.6π1.6\pi. The frequency of this wave is

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  4. Question 4

    4 May 2023 S1

    46
    A progressive wave of frequency 400 Hz is travelling with a velocity 336 m/s. How far apart are the two points which are 60∘60^\circ out of phase?

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  5. Question 5

    4 May 2023 S1

    13
    The distance between two consecutive points with phase difference of 60∘60^\circ in a wave of frequency 500 Hz is 0.6 m. The velocity with which wave is travelling is

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  6. Question 6

    4 May 2023 S2

    19
    A transverse wave travelling along a stretched string has a speed of 30 m/s and a frequency of 250 Hz. The phase difference between two points on the string 10 cm apart at the same instant is

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  7. Question 7

    15 May 2023 S2

    43
    Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of 1.6π1.6\pi. Frequency of this wave is

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  8. Question 8

    19 Apr 2025 S2

    27
    A progressive wave of frequency 400 Hz is travelling with velocity 336 m/s336\,m/s. How far apart are the two points on a wave which are 60∘60^{\circ} out of phase?

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  9. Question 9

    13 Apr 2026 S2

    124
    The distance between two consecutive points with phase difference of 60∘60^\circ in a wave of frequency nn is xx meter. The velocity with which wave is traveling is

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  10. Question 10

    13 May 2026 S1

    123
    Two points on a travelling wave having frequency 500500 Hz and velocity 300300 m/s are 60∘60^\circ out of phase, then the minimum distance between the two points is

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  11. Question 11

    15 May 2026 S2

    124
    Two points separated by 66 cm on a string has phase difference of 60∘60^\circ. If frequency of oscillation is 500500 Hz, the velocity of the wave in ms\dfrac{m}{s} is

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