Download App

Superposition of Waves — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsSuperposition of Waves3 Marks
Question
A string is fixed at the two ends and is vibrating in its fundamental mode. It is known that the two ends will be at rest. Apart from these, is there any position on the string which can be touched so as not to disturb the motion of the string? What will be the answer to this question if the string is vibrating in its first and second overtones?
✓

Answer

Nodes are the points where the vibrating string can be touched without disturbing its motion.
When the string vibrates in its fundamental mode, the string vibrates in one loop. There are no nodes formed between the fixed ends. Hence, there are no point on the string which can be touched without disturbing its motion.

When the string vibrates in its first overtone (second harmonic), there are two loops of the stationary wave on the string. Apart from the two nodes at the two ends, there is now a third node at its centre. Hence, the string can be touched at its centre without disturbing the stationary wave pattern.

When the string vibrates in its second overtone (third harmonic), there are three loops of the stationary wave on the string. So, apart from the two end nodes, there are two additional nodes in between, at distances one-third of the string length from each end. Thus, now the string can be touched at these two nodes.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following in Brief" from Superposition of Waves→Superposition of Waves — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

What should be the diameter of a soap bubble such that the excess pressure inside it is 51.2
Pa? [Surface tension of soap solution $=3.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ ]
→
A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 litres to a volume of 10 litres. In doing so it absorbs 400 J of thermal energy from its surroundings. Determine the change in internal energy of system. 
→
When a resistor of \(5 \Omega\) is connected across the cell, its terminal potential difference is balanced by \(150 cm\) of potentiometer wire and when a resistance of \(10 \Omega\) is connected across cell, the terminal potential difference is balanced by \(175 cm\) same potentiometer wire. Find the balancing length when the cell is in open circuit and the internal resistance of the cell.
→
When a resistance of \(12 ohm\) is connected across a cell, its terminal potential difference is balanced by \(120 cm\) length of potentiometer wire. When the resistance of \(18 ohm\) is connected across the same cell, the balancing length is \(150 cm\). Find the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.
→
Define absolute pressure.
→
A $3 kg$ block, attached to a spring, performs linear SHM with the displacement given by $x =2$ $\cos (50 t ) m$. Find the spring constant of the spring.
→
The emf of a standard cell is 1.5V and is balanced by a length of 300 cm of a potentiometer with a 10 m long wire. Find the percentage error in a voltmeter that balances at 350 cm when its reading is 1.8 V.
→
Explain what you understand by interference of light.
→
How is potential gradient measured? Explain.
→
A toroidally wound coil has an inner radius of $15 \ cm$, an outer radius of $20 \ cm$ and is wound with $1500$ turns of wire. What is the magnitude of the magnetic induction at the centre of the coil when the current in the winding is $10 A$ ?
→