Question:
When a sonometer wire vibrates in the third overtone, the number of antinodes and nodes formed on the wire are respectively
When a sonometer wire vibrates in the third overtone, the number of antinodes and nodes formed on the wire are respectively
Show Hint
Third overtone is the 4th harmonic of a string fixed at both ends.
Updated On: Oct 1, 2026
- \(4,5\)
- \(5,4\)
- \(3,4\)
- \(4,3\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
A sonometer wire is fixed at both ends, so both ends are nodes. The fundamental has 1 loop, the first overtone has 2 loops, and so on.
Step 2: Third overtone:
Third overtone means the 4th harmonic, so there are 4 loops. Each loop contains one antinode, so antinodes = 4.
Step 3: Count nodes:
With both ends as nodes, nodes = antinodes + 1 = 5.
Step 4: Check:
Option (A): 4 antinodes and 5 nodes. Option (B) swaps the numbers. Options (C) and (D) correspond to the 2nd and 3rd harmonic or other modes.
Final Answer:
The 4th harmonic has 4 antinodes and 5 nodes. \[ \boxed{\text{(A) }4,\ 5} \]
A sonometer wire is fixed at both ends, so both ends are nodes. The fundamental has 1 loop, the first overtone has 2 loops, and so on.
Step 2: Third overtone:
Third overtone means the 4th harmonic, so there are 4 loops. Each loop contains one antinode, so antinodes = 4.
Step 3: Count nodes:
With both ends as nodes, nodes = antinodes + 1 = 5.
Step 4: Check:
Option (A): 4 antinodes and 5 nodes. Option (B) swaps the numbers. Options (C) and (D) correspond to the 2nd and 3rd harmonic or other modes.
Final Answer:
The 4th harmonic has 4 antinodes and 5 nodes. \[ \boxed{\text{(A) }4,\ 5} \]
Was this answer helpful?
0
0
Top MHT CET Physics Questions
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- A particle moves along a circle of radius ?$r$? with constant tangential acceleration. If the velocity of the particle is ?$?$? at the end of second revolution, after the revolution has started then the tangential acceleration is
- If $M_z$ = magnetization of a paramagnetic sample, $B$ = external magnetic field, $T$ = absolute temperature, $C$ = curie constant then according to Curie�s law in magnetism, the correct relation is
- In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is
- In a parallel plate capacitor, the capacity increases if
View More Questions
Top MHT CET Vibrating Wire and Frequency Questions
A sonometer wire gives frequency \( f_1 \) with tension \( T_1 \). If the tension is made 4 times greater, what is the new frequency? The frequency of a vibrating wire is related to the tension in the wire by the equation: \[ f \propto \sqrt{T} \] where:
\( f \) is the frequency,
\( T \) is the tension in the wire.If the tension is increased by a factor of 4, how does the frequency change?
- Two uniform strings ' A ' and ' B ' made of steel are made to vibrate under same tension. If the first overtone of ' A ' is equal to second overtone of ' B ' and radius of ' A ' is twice that of ' B '. Then the ratio of length of string ' A ' to that of ' B ' is
- Two uniform strings ' A ' and ' B ' made of steel are made to vibrate under same tension. If the first overtone of ' A ' is equal to second overtone of ' B ' and radius of ' A ' is twice that of ' B '. Then the ratio of length of string ' A ' to that of ' B ' is
- A wire of length L , diameter ' d ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration $\text{n}_\text{A}$. Another wire of length 2 L , tension 2 T , density 2 e and diameter 3 d has fundamental frequency of vibration $\text{n}_\text{B}$. The ratio $\text{n}_\text{B} : \text{n}_\text{A}$ is
- In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions