Answer
Verified
427.5k+ views
Hint: To solve this problem we will substitute the given values in the sonometer formula.
We need to use a sonometer working formula. i.e. \[{f_n} = \dfrac{n}{{2l}}\sqrt {\dfrac{T}{m}} \], where, \[{f_n}\] is the frequency of \[nth\]mode, \[n\] is the mode number, \[l\] is the length of the wire, \[T\] is the tension in the wire, \[m\] is the linear mass density or mass per unit length of the wire.
Complete step-by-step answer:
If the tension reduced to half, and length becomes \[{l_1}\] then from the above condition,
\[\dfrac{1}{{2l}}\sqrt {\dfrac{T}{m}} = \dfrac{2}{{2{l_1}}}\sqrt {\dfrac{T}{{2m}}} \]
As n is a constant value, we neglected n in the formula.
$ \Rightarrow {l_1} = 1\sqrt 2 $
Thus, the correct answer to this question is option (b).
Note: A sonometer is a device for demonstrating the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. These relationships are usually called Mersenne's laws after Marin Mersenne (1588-1648), who investigated and codified them. It is used to measure the tension, frequency or density of vibrations. In the field of medicine, it is used to test both hearing and bone density. The vibrations produced by the string works under the principle of resonance and is often represented as sinusoidal waves. This is very useful.
We need to use a sonometer working formula. i.e. \[{f_n} = \dfrac{n}{{2l}}\sqrt {\dfrac{T}{m}} \], where, \[{f_n}\] is the frequency of \[nth\]mode, \[n\] is the mode number, \[l\] is the length of the wire, \[T\] is the tension in the wire, \[m\] is the linear mass density or mass per unit length of the wire.
Complete step-by-step answer:
If the tension reduced to half, and length becomes \[{l_1}\] then from the above condition,
\[\dfrac{1}{{2l}}\sqrt {\dfrac{T}{m}} = \dfrac{2}{{2{l_1}}}\sqrt {\dfrac{T}{{2m}}} \]
As n is a constant value, we neglected n in the formula.
$ \Rightarrow {l_1} = 1\sqrt 2 $
Thus, the correct answer to this question is option (b).
Note: A sonometer is a device for demonstrating the relationship between the frequency of the sound produced by a plucked string, and the tension, length and mass per unit length of the string. These relationships are usually called Mersenne's laws after Marin Mersenne (1588-1648), who investigated and codified them. It is used to measure the tension, frequency or density of vibrations. In the field of medicine, it is used to test both hearing and bone density. The vibrations produced by the string works under the principle of resonance and is often represented as sinusoidal waves. This is very useful.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
10 examples of evaporation in daily life with explanations
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Why is there a time difference of about 5 hours between class 10 social science CBSE