Question:
A tuning fork of frequency '\(n\)' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are \(l_1\) and \(l_2\), the speed of sound in air is (neglect end correction)
A tuning fork of frequency '\(n\)' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are \(l_1\) and \(l_2\), the speed of sound in air is (neglect end correction)
Show Hint
Consecutive resonances in a closed tube differ by half a wavelength.
Updated On: Oct 1, 2026
- \(2n(l_2-l_1)\)
- \(n(l_2-l_1)\)
- \(\frac{n}{2}(l_2-l_1)\)
- \(\frac{2n}{(l_2-l_1)}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
A tube closed at one end (by water) resonates when its air column length is an odd multiple of \(\frac\lambda4\). The first two shortest resonating lengths are \(l_1 = \frac\lambda4\) and \(l_2 = \frac{3\lambda}{4}\) (neglecting end correction).
Step 2: Subtract:
\[ l_2 - l_1 = \frac{3\lambda}{4} - \frac\lambda4 = \frac\lambda2 \Rightarrow \lambda = 2(l_2 - l_1) \]
Step 3: Speed:
\[ v = n\lambda = 2n(l_2 - l_1) \]
Step 4: Why the other options are wrong.
\(n(l_2 - l_1)\) would be the speed if \(l_2 - l_1\) were a full wavelength. \(\frac n2(l_2 - l_1)\) and \(\frac{2n}{l_2 - l_1}\) are not valid: the last has wrong units.
Final Answer:
The speed of sound is \(2n(l_2 - l_1)\), option (A). \[ \boxed{2n(l_2-l_1)} \]
A tube closed at one end (by water) resonates when its air column length is an odd multiple of \(\frac\lambda4\). The first two shortest resonating lengths are \(l_1 = \frac\lambda4\) and \(l_2 = \frac{3\lambda}{4}\) (neglecting end correction).
Step 2: Subtract:
\[ l_2 - l_1 = \frac{3\lambda}{4} - \frac\lambda4 = \frac\lambda2 \Rightarrow \lambda = 2(l_2 - l_1) \]
Step 3: Speed:
\[ v = n\lambda = 2n(l_2 - l_1) \]
Step 4: Why the other options are wrong.
\(n(l_2 - l_1)\) would be the speed if \(l_2 - l_1\) were a full wavelength. \(\frac n2(l_2 - l_1)\) and \(\frac{2n}{l_2 - l_1}\) are not valid: the last has wrong units.
Final Answer:
The speed of sound is \(2n(l_2 - l_1)\), option (A). \[ \boxed{2n(l_2-l_1)} \]
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 CurieοΏ½s 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 Sound Wave Questions
- How does the dynamic resistance of diode vary with temperature?
- Sound waves of frequency $600\ \text{Hz}$ fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound $=300\ \text{ms}^{-1}$)}
- A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of \(l_c : l_o\) is [\(l_c = \text{vibrating length of closed pipe}, l_o = \text{vibrating length of open pipe}\)]
- A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of \(l_c : l_o\) is [\(l_c = \text{vibrating length of closed pipe}, l_o = \text{vibrating length of open pipe}\)]
- An organ pipe has fundamental frequency $80\text{ Hz}$ . If its one end is closed, the frequencies produced will be (in $\text{Hz}$ ) (Neglect end correction)}
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