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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
- a)1 kg
- b)2 kg
- c)4 kg
- d)16 kg
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A sonometer wire supports a 4 kg load and vibrates in fundamental mod...
Load supported by sonometer wire = 4 kg
Tension in sonometer wire= 4 g
If µ = mass per unit length
then frequency
⇒ 
When length is doubled, i.e., /' = 2l
Let new load = L
As, v' = v
∴ 
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A sonometer wire supports a 4 kg load and vibrates in fundamental mod...
Problem:
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 the fundamental mode, the load should be changed to
a) 1 kg
b) 2 kg
c) 4 kg
d) 16 kg
Solution:
Concept:
In a sonometer wire, the fundamental frequency of vibration is given by the formula:
f = (1/2L) * √(T/μ)
where f is the frequency, L is the length of the wire, T is the tension in the wire, and μ is the linear mass density of the wire.
Given:
Original load = 4 kg
Original frequency = 416 Hz
Length of the wire is doubled
Approach:
We need to find the new load that should be applied to the wire in order to maintain the fundamental frequency when the length of the wire is doubled.
To do this, we can use the formula for the fundamental frequency and compare the original and new situations.
Calculations:
Step 1: Find the original length of the wire (L) using the formula for the fundamental frequency:
f = (1/2L) * √(T/μ)
Rearranging the formula:
L = (1/2f) * √(T/μ)
Substituting the given values:
L = (1/2 * 416) * √(T/μ)
Step 2: Find the new length of the wire (L') when it is doubled:
L' = 2 * L
Step 3: Substitute the values of L' and solve for the new load (T'):
f = (1/2L') * √(T'/μ)
Substituting the values:
416 = (1/2 * 2L) * √(T'/μ)
Simplifying:
416 = L * √(T'/μ)
Substituting the value of L from Step 1:
416 = [(1/2 * 416) * √(T/μ)] * √(T'/μ)
Simplifying further:
416 = 1/2 * √(T'/μ) * √(T/μ)
Substituting the given values:
416 = 1/2 * √(T'/μ) * √(4 kg / μ)
Simplifying:
416 = 1/2 * √(T'/μ) * 2
416 = √(T'/μ)
Squaring both sides:
(416)^2 = (T'/μ)
Simplifying:
173,056 = T'/μ
Step 4: Find the new load (T'):
T' = 173,056 * μ
Substituting the given value of μ (linear mass density of the wire):
T' = 173,056 * (4 kg/m)
Simplifying:
T' = 692,224 kg
Converting the load to kg:
T' = 692,224 kg * 9.8 m/s^2
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 the fundamental mode, the load should be changed to
a) 1 kg
b) 2 kg
c) 4 kg
d) 16 kg
Solution:
Concept:
In a sonometer wire, the fundamental frequency of vibration is given by the formula:
f = (1/2L) * √(T/μ)
where f is the frequency, L is the length of the wire, T is the tension in the wire, and μ is the linear mass density of the wire.
Given:
Original load = 4 kg
Original frequency = 416 Hz
Length of the wire is doubled
Approach:
We need to find the new load that should be applied to the wire in order to maintain the fundamental frequency when the length of the wire is doubled.
To do this, we can use the formula for the fundamental frequency and compare the original and new situations.
Calculations:
Step 1: Find the original length of the wire (L) using the formula for the fundamental frequency:
f = (1/2L) * √(T/μ)
Rearranging the formula:
L = (1/2f) * √(T/μ)
Substituting the given values:
L = (1/2 * 416) * √(T/μ)
Step 2: Find the new length of the wire (L') when it is doubled:
L' = 2 * L
Step 3: Substitute the values of L' and solve for the new load (T'):
f = (1/2L') * √(T'/μ)
Substituting the values:
416 = (1/2 * 2L) * √(T'/μ)
Simplifying:
416 = L * √(T'/μ)
Substituting the value of L from Step 1:
416 = [(1/2 * 416) * √(T/μ)] * √(T'/μ)
Simplifying further:
416 = 1/2 * √(T'/μ) * √(T/μ)
Substituting the given values:
416 = 1/2 * √(T'/μ) * √(4 kg / μ)
Simplifying:
416 = 1/2 * √(T'/μ) * 2
416 = √(T'/μ)
Squaring both sides:
(416)^2 = (T'/μ)
Simplifying:
173,056 = T'/μ
Step 4: Find the new load (T'):
T' = 173,056 * μ
Substituting the given value of μ (linear mass density of the wire):
T' = 173,056 * (4 kg/m)
Simplifying:
T' = 692,224 kg
Converting the load to kg:
T' = 692,224 kg * 9.8 m/s^2
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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 toa)1 kgb)2 kgc)4 kgd)16 kgCorrect answer is option 'D'. Can you explain this answer?
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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 toa)1 kgb)2 kgc)4 kgd)16 kgCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 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 toa)1 kgb)2 kgc)4 kgd)16 kgCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 toa)1 kgb)2 kgc)4 kgd)16 kgCorrect answer is option 'D'. Can you explain this answer?.
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