Tag: free, forced and damped oscillations

Questions Related to free, forced and damped oscillations

In Melde's experiment four loops were formed on a string under tension T. When the tension in the string was increased by $3g$, two loops were observed. The original tension T in the string is :

  1. $2 g$

  2. $1 g$

  3. $3 g$

  4. $4 g$


Correct Option: B

In Meldes experiment, the tuning fork is arranged in the parallel position. During $200$ vibrations of the tuning fork, the string ccompletes vibrations

  1. $200$

  2. $100$

  3. $50$

  4. $25$


Correct Option: A

If there are six loops for 1 m length in transverse mode of Melde's experiment., the no. of loops in longitudinal mode under otherwise identical condition would be

  1. 3

  2. 6

  3. 12

  4. 8


Correct Option: A
Explanation:

One cycle of up and down vibration for transverse waves on the string is two cycles of string tension increase and decrease. The tension is maximum both at the loops’ maximum up position and again at maximum down position. Therefore, in longitudinal drive mode, since the string tension increases and decreases once per tuning fork vibration, it takes one tuning fork vibration to move the string loop to maximum up position and one to move it to maximum down position. This is two tuning fork vibrations for one up and down string vibration, so the tuning fork frequency is half the string frequency.
Hence, the number of loops in longitudinal mode(tuning fork) is half of that of transverse mode(string).

In Melde's experiment, the string vibrates in seven segments under tension of $9\space gm-wt$. If string is to be vibrated in three segments then the tension required will be

  1. $1.4\space gm$-$wt$

  2. $13\space gm$-$wt$

  3. $49\space gm$-$wt$

  4. $61\space gm$-$wt$


Correct Option: C
Explanation:
The frequency is the same before and after changing the Tension and the number of loops.
From the formula $f = \dfrac{n}{2L}\sqrt{(T/m)}$, we get
$\dfrac{7}{2L}\sqrt{(9/m)} = \dfrac{3}{2L}\sqrt{(T'/m)}$
=>$T' = 49 gm-wt$

In Melde's experiment, frequency can _______ by ________number of loops of the  string.

  1. increase ,increasing

  2. increase, decreasing

  3. decrease, increasing

  4. decrease, decreasing


Correct Option: A

The  apparatus of Melde's experiment can be used to test the relationship between 
A. Tension
B. Mass per unit length 
C. Frequency
D. Wavelength
Choose the most appropriate option among the following?

  1. A, B only

  2. A, C only

  3. A,B,C only

  4. All of the above


Correct Option: D

The fundamental frequency of sonometer wire is 600Hz. When length wire is shorted by 25%, the frequency of ${ 1 }^{ st }$ overtone will be

  1. 800 Hz

  2. 1200 HZ

  3. 1600 Hz

  4. 2000 Hz


Correct Option: C

In Melde's experiment when longitudinal position is used 4 loops are formed on string under tension of 16 g-wt . Now the string is replaced by another string of same material but of diameter half of the previous diameter and length half that of the original strings . What should be the tension in the string to obtain 2 loops on the strings , when B position is used ? 

  1. 16 g-wt

  2. 32 g-wt

  3. 8 g-wt

  4. 4 g-wt


Correct Option: B

A string of length $36cm$ was in unison with a fork of frequency $256Hz$. It was in unison with another fork when the vibrating length was $48cm$, the tension being unaltered. The frequency of second fork is   

  1. $212Hz$

  2. $320Hz$

  3. $384Hz$

  4. $192Hz$


Correct Option: D
Explanation:

$f=\dfrac{v }{2L}$
$v =f(2\ L)$
$=256\times 2\times 36$
$=18432\ cm/s.$


wave velocty remains same
$f=\dfrac{v }{2L}$
$=\dfrac{18432}{2\times 48}$
$=192\ Hz.$

The total mass of a wire remains constant on stretching the length of wire to four times. It's frequency will become:

  1. 4 times

  2. 1/2 times

  3. 8 times

  4. $\sqrt{2}$ times


Correct Option: B
Explanation:

Frequency, $f=\dfrac{1}{2l}\sqrt{\dfrac{t}{\mu }}$


Length is made four times, but mass is same.

$\Rightarrow$ Mass per unit length is $\mu'=\dfrac{\mu }{4}$

$\Rightarrow f'=\dfrac{1}{2(4l)}\sqrt{\dfrac{t}{\frac{\mu }{4}}}$$=\dfrac{2}{2(4l)}\sqrt{\dfrac{t}{\mu }}$ 

$\Rightarrow \dfrac{f'}{f}=\dfrac{1}{2}$

$\Rightarrow f'=\dfrac{f}{2}$