Question

A tuning fork of frequency $480Hz$is used to vibrate a sonometer wire having natural frequency $240Hz$ . The wire will vibrate with a frequency of
A) $240Hz$
B) $480Hz$
C) $720Hz$
D) will not vibrate

Answer 1

Hint: Here in this question, firstly we have to know that, The length of the wire is measured as the sonometer is first set to coincide with a standard fork of known frequency. It is now adjusted to the unidentified fork by only changing the length while keeping the tension constant. Together, a sonometer wire and a tuning fork can create 5 beats per second when the wire is either 95 cm or 100 cm in length. Out of which, we have to find the frequency of the vibration of the wire.



Complete answer:

As we know, when we use sonometer wire with a tuning fork it forms a Simple Harmonic motion as from which the vibration which is produced from the tuning fork will get transmitted to the wire.
As from which we get that,
The frequency of the wire's vibration will match the frequency of the periodic external force created by the tuning force. As a result, the wire will vibrate at $480Hz$ .
Therefore, the correct answer is $480Hz$ .

Hence, the correct answer is Option B.





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.