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The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio of 1 : 3 : 5?              [NEET Kar. 2013]
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Top Rankers answered
Answer :- a
Solution :- Fundamental frequency (v) = 1/L
As the fundamental frequencies are in the ratio of 1:3:5,
L1 : L2 : L3 = 1/1 : 1/3 : 1/5  => 15 : 5 : 3
Let x be the common factor , then
15x + 5x + 3x = L = 100
23x = 100 
=> x = 100/23
L1 = 15*100/23 = 1500/23
L2 = 5*100/23 = 500/23
L3 = 3*100/23 = 300/23
The bridge should be placed from A at (1500/23 , 2000/23)

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170 sec.The frequency of the wave is [1998]
  • a)
    1.47 Hz
  • b)
    0.36 Hz
  • c)
    0.73 Hz
  • d)
    2.94 Hz
Correct answer is option 'A'. Can you explain this answer?

Sinjini Patel answered
Given:
- Time required for a particular point to move from maximum displacement to zero displacement = 0.170 sec

To find:
- Frequency of the wave

Formula:
- Frequency (f) = 1 / Time period (T)

Explanation:
The time period is the time taken for one complete cycle of the wave. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is half of the time period.

Given that the time required for this movement is 0.170 sec, we can find the time period as follows:

- Time period (T) = 2 * 0.170 sec = 0.340 sec

Now, we can calculate the frequency using the formula:

- Frequency (f) = 1 / Time period (T)
- Frequency (f) = 1 / 0.340 sec
- Frequency (f) ≈ 2.94 Hz

Therefore, the frequency of the wave is approximately 2.94 Hz.

Answer:
The correct answer is option A) 1.47 Hz.

Two vibrating tuning for ks produce progressive waves given by y1 = 4 sin 500 πt and y2 = 2 sin 506 πt. Number of beats produced per minute is [2 00 5]
  • a)
    360
  • b)
    180
  • c)
    60
  • d)
    3
Correct answer is option 'B'. Can you explain this answer?

Krish Saha answered
Equation of progressive wave is given by y = A sin2πft
Given y1 = 4sin500 πt and y2 = 2sin506πt.
Comparing the given equations with equation of progressive wave, we get 2f1 = 500 ⇒  f1 = 250 2f2 = 506 ⇒ f2 = 253
Beats = f2– f1 = 253 – 250 = 3 beats/sec = 3 × 60 = 180 beats/minute.

A cylindrical resonance tube open at both ends, has a fundamental frequency, f, in air. If half of the length is dipped vertically in water, the fundamental frequency of the air column will be
  • a)
    2f
  • b)
    3f/2 [1997]
  • c)
    f
  • d)
    f/2
Correct answer is option 'C'. Can you explain this answer?

Diya Datta answered
Fundamental frequency of open pipe,
When half of tube is filled with water, then the length of air column becomes half
and the pipe becomes closed.
So,  new fundamental frequency
Clearly f ' = f.

Resonance is an example of [1999]
  • a)
    tuning fork
  • b)
    forced vibration
  • c)
    free vibration
  • d)
    damped vibration
Correct answer is option 'B'. Can you explain this answer?

We know that if frequency of an external forced  oscillation is equal to the natural frequency of the body, then amplitude of the forced oscillation of the body becomes very large. This phenomenon is known as resonant vibration. Therefore, resonance is an example of forced vibration.

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