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String Fixed at Both Ends

A sonometer w...

Question

A sonometer wire of length l vibrates in fundamental mode when excited by a tunning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

A

vibrates with frequency of 416 Hz

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B

vibrates with frequency of 208 Hz

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C

vibrates with frequency of 832 Hz

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D

stop vibrating

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Solution

The correct option is A vibrates with frequency of 416 Hz
since the wire is being excited by the tunning fork of frequency $416$ Hz then wire of sonometer will always vibrate at frequency $416$ Hz the change in length will only effect its fundamental frequency.
so the answer is A.

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Q. A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will
(a) vibrate with a frequency of 416 Hz
(b) vibrate with a frequency of 208 Hz
(c) vibrate with a frequency of 832 Hz
(d) stop vibrating.

Q. A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

Q. A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

Q. A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tuning fork of frequency 416. Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to
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