Two identical straight wires are stretched so as to produce 6 beats/s when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by $T_1,T_2$ the higher and the lower initial tension in the strings, then it could be said that while making the above changes in tension
- $T_2$ was decreased
- $T_2$ was increased
- $T_1$ was decreased
- $T_1$ was increased
The Correct Option is C
Solution and Explanation
$\therefore\hspace25mm v_1 >v_2$
or $\hspace25mm f_1 > f_2$
and $\hspace20mm f_1 - f_2=6\, Hz$
Now, if $T_1$ is increased, $f_1$ will increase or $f_1 - f_2$ will
increase. Therefore, (d) option is wrong.
If $T_1$ is decreased, $f_1$ will decrease and it may be possible that
now $f_2-f_1$ become 6 Hz.Therefore, (c) option is correct.
Similarly, when $T_2$ is increased, $f_2$ will increase and again
$f_2-f_1$ may become equal to 6 Hz. So, (b) is also correct.
But (a) is wrong.
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Concepts Used:
Simple Harmonic Motion
Simple Harmonic Motion is one of the most simple forms of oscillatory motion that occurs frequently in nature. The quantity of force acting on a particle in SHM is exactly proportional to the displacement of the particle from the equilibrium location. It is given by F = -kx, where k is the force constant and the negative sign indicates that force resists growth in x.
This force is known as the restoring force, and it pulls the particle back to its equilibrium position as opposing displacement increases. N/m is the SI unit of Force.
Types of Simple Harmonic Motion
Linear Simple Harmonic Motion:
When a particle moves to and fro about a fixed point (called equilibrium position) along with a straight line then its motion is called linear Simple Harmonic Motion. For Example spring-mass system
Conditions:
The restoring force or acceleration acting on the particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.
- – displacement of particle from equilibrium position.
- – Restoring force
- - acceleration
Angular Simple Harmonic Motion:
When a system oscillates angular long with respect to a fixed axis then its motion is called angular simple harmonic motion.
Conditions:
The restoring torque (or) Angular acceleration acting on the particle should always be proportional to the angular displacement of the particle and directed towards the equilibrium position.
Τ ∝ θ or α ∝ θ
Where,
- Τ – Torque
- α angular acceleration
- θ – angular displacement