The Question is from NEET guide , and it was created by the author NAGA SAI

Question

A sonometer wire is in unison with a tuning fork of frequency 300 Hz.  If the tension in the wire is increased, the length of the wire must be ______ to bring it back into unison with the tuning fork.

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
	**Primary Concept**: Resonance and the fundamental frequency of a stretched string.
	**Related Topics**: Waves, Sound, Vibrations, Musical Instruments
	**Prerequisites**: Understanding of wave properties, frequency, and the relationship between tension, length, and frequency in a vibrating string.
## SOLUTION PATHWAY
**Given Information**:
	* A sonometer wire is in unison (same frequency) with a tuning fork of 300 Hz.
	* The tension in the wire is increased.
**Method & Steps**:
	1. **Recall the relationship between frequency, tension, and length of a vibrating string:**
		Reasoning: The fundamental frequency ($f$) of a vibrating string is given by the formula $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$, where $L$ is the length, $T$ is the tension, and $\mu$ is the linear mass density (mass per unit length).
		Formula/Rule: $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$
	2. **Analyze the effect of increased tension:**
		Working: If the tension ($T$) increases, the frequency ($f$) also increases, as they are directly proportional.
		Key Point: We want to bring the wire back to the original frequency (300 Hz) of the tuning fork.
	3. **Determine the necessary change in length:**
		Result: Since the frequency has increased due to the higher tension, we need to decrease the frequency to bring it back to 300 Hz.  According to the formula, increasing the length ($L$) will decrease the frequency ($f$), as they are inversely proportional.
		Verification: By increasing the length, we compensate for the increased tension, bringing the frequency back down to the original 300 Hz and back into unison with the tuning fork.
## OPTION ANALYSIS
[A] ✓: Increased: Correct. Increasing the length lowers the frequency to compensate for the increased tension, restoring unison.
[B] :x: Decreased: Incorrect. Decreasing the length would further increase the frequency, moving it further away from the tuning fork's frequency.
[C] :x: Kept the same: Incorrect. If the length remains the same, the increased tension will result in a higher frequency, and the wire will no longer be in unison with the tuning fork.
[D] :x: Doubled: Incorrect. While increasing the length is correct, doubling may not be the exact adjustment needed. The precise change in length depends on the specific change in tension.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing the relationship between tension and frequency: Remember that higher tension leads to higher frequency.
		2. Forgetting the inverse relationship between length and frequency: Remember that longer strings have lower frequencies.
	**Quick Tips**:
		1. Visualize the string: Imagine tightening a guitar string (increasing tension) makes the pitch higher (higher frequency).  To lower the pitch back down, you would need to make the string longer.
		2. Remember the formula: $f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$  This clearly shows the relationships between frequency, length, and tension.

NAGA SAI · Answer

The correct Option is "increased"

NAGA SAI · Answer

decreased

NAGA SAI · Answer

kept the same

NAGA SAI · Answer

doubled

NEET Questions

Select Subject

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company