MCQ
A taut string at both ends vibrates in its $n^{th}$ overtone. The distance between adjacent Node and Antinode is found to be $'d'$. If the length of the string is $L,$ then
- ✓$L = 2d (n + 1)$
- B$L = d (n + 1)$
- C$L = 2dn$
- D$L = 2d (n - 1)$
✓
Answer
Correct option: A.
$L = 2d (n + 1)$
a
For a taut string between two ends$:$
For a taut string between two ends$:$
$n^{\text {th}}$overtone$=(n+1)$harmonic
$n^{\text {th}}$overtone$=(n+1)$harmonic
$\frac{(n+1)}{2} \lambda=L \ldots \ldots \ldots .(L=\text {lengtho $f$ string}) \ldots \ldots \ldots .(1)$
Distance between node and antinode is given by $\frac{\lambda}{4}$ which is equal to $”d”$ according to
the question. $\left(\frac{\lambda}{4}=d o r \lambda=4 d\right)$
Substituting the value of $\mathrm{d}$ in equation $(1)$
$\frac{(n+1) 4 d}{2}=L$
$(n+1) 2 d=L$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Consider a block of conducting material ofresistivity '$\rho$' shown in the figure. Current '$I$' enters at '$A$' and leaves from '$D$'. We apply superp osition principle to find voltage '$\Delta V$ ' developed between '$B$' and '$C$'. The calculation is done in the following steps:
$(i)$ Take current '$I$' entering from '$A$' and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculatefield $E(r)$ at distance '$r$' from $A$ by using Ohm's law $E = \rho j$, where j is the current per unit area at '$r$'.
$(iii)$ From the '$r$' dependence of $E(r)$, obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i), (ii)$ and $(iii)$ for current '$I$' leaving '$D$' and superpose results for '$A$' and '$D$'.
→$(i)$ Take current '$I$' entering from '$A$' and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculatefield $E(r)$ at distance '$r$' from $A$ by using Ohm's law $E = \rho j$, where j is the current per unit area at '$r$'.
$(iii)$ From the '$r$' dependence of $E(r)$, obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i), (ii)$ and $(iii)$ for current '$I$' leaving '$D$' and superpose results for '$A$' and '$D$'.
For current entering at $A$, the electric field at a distance '$r$'
from $A$ is
A particle moves in the $xy$ plane with a constant acceleration $'g'$ in the negative $y$-direction. Its equation of motion is $y = ax-bx^2$, where $a$ and $b$ are constants. Which of the following are correct?
→An optical device is constructed by fixing three identical convex lenses of focal lengths $10 \,cm$ each inside a hollow tube at equal spacing of $30 \,cm$ each. One end of the device is placed $10 cm$ away from a point source. ........... $cm$ the image shift when the device is moved away from the source by another $10 \,cm$ ?
→A voltmeter of resistance $20000\,\Omega$ reads $5$ volt. To make it read $20$ volt, the extra resistance required is
→A simple pendulum, made of a string of length $l$ and a bob of mass $m$ , is released from a small angle $\theta_0$. It strikes a block of mass $M$, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $\theta_1$. Then $M$ is given by
→In a step-up transformer the voltage in the primary is $220\,V$ and the current is $5\,A$. The secondary voltage is found to be $22000\,V$. The current in the secondary (neglect losses) is......$A$
→Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point $O$ and perpendicular to the plane of the figure at a distance of $x(>> a)$ from $O$ is
→The percentage errors in quantities $P, Q, R$ and $S$ are $0.5\%,\,1\%,\,3\%$ and $1 .5\%$ respectively in the measurement of a physical quantity $A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}$ . the maximum percentage error in the value of $A$ will be $......... \%$
→Find out current in $3\,\Omega $ resistance in given circuit
→Which of the following statements is true