In a stationary wave along a string the strain is
Show Hint
In a stationary wave along a string, the strain is maximum at the node due to the interference of two opposite waves.
- zero at the antinodes
- maximum at the antinodes
- zero at the nodes
- maximum at the nodes
Approach Solution -2
The correct answer is Option is D) maximum at the nodes
Real Life Applications
Real life applications of strain in stationary waves:
1) The strain in the wings of an airplane is what allows it to fly.
2) The strain in the cables of a suspension bridge is what prevents it from collapsing.
3) The strain in the sails of a boat is what allows it to sail.
4) In the musical instruments
5) The strain in these waves shows the cause of ground shaking induced by Earthquake
Question can also be asked as
- What is the strain of a stationary wave along a string?
- What are the nodes in stationary waves?
- Why the strain is zero at antinodes?
- Is the strain maximum at the nodes or the antinodes of a stationary wave along a string?
Approach Solution -3
The correct answer is Option is D) maximum at the nodes
Stationary waves are formed when two waves of the same frequency and amplitude travel in opposite directions along a string. In a stationary wave, certain points called nodes appear to be stationary, while other points called antinodes undergo maximum displacement.
Strain in a Stationary Wave
- Strain refers to the deformation or elongation experienced by a material when subjected to an external force.
- In a stationary wave, strain is the maximum at the nodes, which are the points of zero displacement.
- At the nodes, two opposite waves meet and interfere, causing a cancellation of displacement and resulting in maximum strain.
Also Check:
| Related Concepts | ||
|---|---|---|
| Types of Waves | Transverse Waves | Reflection of Waves |
| Doppler effect | Reflection of Light | Wave Motion |
Forces at the Node
- The strain at the nodes is a result of the forces acting on the string at those points.
- Two opposite waves with equal amplitude and frequency meet at the node, creating destructive interference.
- The opposing waves generate equal and opposite forces at the node, leading to a maximum strain on the string.
Node Behavior
- Nodes are points of minimum displacement in a stationary wave.
- At the nodes, the amplitude of the wave is zero, and the string remains relatively still.
- The presence of nodes in a stationary wave pattern helps define its shape and determine the wavelength.
In a stationary wave on a string, strain is maximum at the nodes due to the destructive interference of two opposite waves. The strain at the nodes is a result of the opposing forces acting on the string.
Learn with videos:
Top Questions on Waves
- Let \( \lambda_e \), \( \lambda_p \), and \( \lambda_d \) be the wavelengths associated with an electron, a proton, and a deuteron, all moving with the same speed. Then the correct relation between them is:
- A person can hear a sound of frequency
- Which of the following statements are correct?
(i) Velocity of sound waves is greater in solids than liquids.
(ii) Velocity of sound waves in vacuum is 330 m/s.
(iii) Sound waves are longitudinal waves.
(iv) Velocity of sound waves in vacuum is zero. - If a travelling wave is given by \( y(x, t) = 0.5 \sin(70.1x - 10\pi t) \), where \( x \) and \( y \) are in metres, the time \( t \) is in seconds, then the frequency of the wave is
- The path difference between two waves given by the equations \( y_1 = a_1 \sin\left(\omega t - \frac{2\pi x}{\lambda}\right) \) and \( y_2 = a_2 \sin\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right) \) is
Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave