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A vibrator makes \( 150 \mathrm{cm} \) of a string to vibrate in 6 loops in the longitudinal arrangement when it is stretched by 150 N. The entire length of the string is then weighed and is found to weigh \( 400 \mathrm{mg} \) Then This question has multiple correct options

1. Frequency of the vibrator is 3 \( \mathrm{kHz} \)
2. Frequency of the vibrator is \( 1.5 \mathrm{kHz} \)
3. Distance between two nodes is \( 25 \mathrm{cm} \)
4. Distance between two nodes is 33 cm

Correct answer: Distance between two nodes is \( 25 \mathrm{cm} \)

Solution

In a standing wave, each loop is half a wavelength, so 6 loops in 150 cm means one loop is 25 cm. The distance between adjacent nodes is also half a wavelength, so it is 25 cm.

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