Question

Arrange the following steps in a sequential order to prove the law of length in vibrating stretched strings.
(a)At a particular length ‘\[{l_1}\]’, the wire between the bridges vibrates with maximum amplitude and this is confirmed by the flying away of a small paper rider placed on the string.
(b)Excite a tuning fork of frequency ‘\[{n_1}\]’ and keep it on a sonometer table between the bridges and adjust the distance between the bridges (from minimum to maximum).
(c)The first law of vibrating stretched strings is verified by showing \[{n_1}{l_1} = {n_2}{l_2}\].
(d)The procedure is repeated by taking another tuning fork of frequency ‘\[{n_2}\]’ and the resonating length ‘\[{l_2}\]’ is obtained.
A. b a d c
B. a b c d
C. b c a d
D. b a c d

Answer 1

Hint: Recall the concept of law of length in vibrating stretched strings. Remind the experiment to prove the law of length in vibrating stretched strings step by step and determine the order of the experiment from the given options.

Complete step by step answer:
The law of length in vibrating stretched strings gives the relation between the frequency of the sound produced with the length of the wire used in the experiment.

The sequential steps in the experiment to prove the law of length in vibrating stretched strings are as follows:

Excite a tuning fork of frequency ‘\[{n_1}\]’ and keep it on a sonometer table between the bridges and adjust the distance between the bridges (from minimum to maximum).

At a particular length ‘\[{l_1}\]’, the wire between the bridges vibrates with maximum amplitude and this is confirmed by the flying away of a small paper rider placed on the string.

The procedure is repeated by taking another tuning fork of frequency ‘\[{n_2}\]’ and the resonating length ‘\[{l_2}\]’ is obtained.

The first law of vibrating stretched strings is verified by showing \[{n_1}{l_1} = {n_2}{l_2}\].

Therefore, the correct sequence for the experiment to prove the law of length in vibrating strings is b a d c.

So, the correct answer is “Option A”.

Additional Information:
According to the law of vibrating strings, if the tension and the linear density of the string are kept constant, the fundamental frequency of vibration of the string is inversely proportional to the length of the string.

Note:
Since the fundamental frequency of vibration is inversely proportional to the length of the string, the relation \[{n_1}{l_1} = {n_2}{l_2}\] is obtained for the two lengths of the strings and corresponding frequencies as the product of two quantities in inverse relation is constant.