Question

A sonometer wire of length l vibrates in fundamental mode when excited by a tunning fork of frequency $416Hz$ . If the length is doubled keeping other things same, the string will
A) Vibrates with frequency of $416Hz$
B) Vibrates with frequency of $208Hz$
C) Vibrates with frequency of $832Hz$
D) Stop vibrating

Answer 1

Hint: Here in this question, we have to find the vibrations of string when the length is doubled, As for which we have to know that, A wave is the vibration of a string. A vibrating string produces a sound with a constant frequency, or pitch, due to resonance. If the string's length or tension are properly adjusted. And in this question our length is doubled for which some changes may take place.



Complete answer:

As from the question, the frequency of the Tuning fork is $416Hz$. Here the only change take place in this is the length is converted into
$l \to 2l$
As from which, only the changes take place between the path of frequency not any other changes take place in the unit number of frequency.
As from which, The wire of the sonometer will always vibrate at frequency $416Hz$ because it is being activated by the tuning fork, and any change in length will only affect its basic frequency.
From the above conclusion, we get that the string will remain with the frequency of $416Hz$ .
Therefore, the correct answer is that the string will vibrate with a frequency of $416Hz$ .
Hence, the correct option is (A).


Hence, the correct option is (A).


Note: We all should know that, A stretched string's length, linear mass density, frequency, and tension are all essentially studied with a sonometer. Devices based on the resonance theory include sonometers. It is utilized to establish the tuning fork's frequency as well as the rules of vibration of stretched strings.