Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, freq

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14.Waves and Sound

medium

Show that when a string fixed at its two ends vibrates in $1$ loop, $2$ loops, $3$ loops and $4$ loops, the frequencies are in the ratio $1 : 2 : 3 : 4$.

Option A

Option B

Option C

Option D

Solution

In case of stationary waves, frequency in the $n^{\text {th }}$ mode of vibration is, $f_{n}=\frac{n v}{2 \mathrm{~L}} \quad$ (Where $v=\sqrt{\frac{\mathrm{T}}{\mu}}=$ speed of

transverse wave in stretched string)

$\therefore f_{n} \propto n$

$\Rightarrow f_{1}: f_{2}: f_{3}: f_{4}=1: 2: 3: 4$

Standard 11

Physics

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. if the first overtone of $ A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is

medium

A second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are respectively

easy

A clamped string is oscillating in $n^{th}$ harmonic, then

normal

Two perfectly identical wires are in unison. When the tension in one wire is increased by $1\%$, then on sounding them together $3$ beats are heard in $2 \,sec$. The initial frequency of each wire is …. ${\sec ^{ – 1}}$

easy

A string is stretched between fixed points separated by $75.0\,\, cm.$ It is observed to have resonant frequencies of $420\,\, Hz$ and $315\,\, Hz$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is …. $Hz$

medium

(AIPMT-2015)

Show that when a string fixed at its two ends vibrates in $1$ loop, $2$ loops, $3$ loops and $4$ loops, the frequencies are in the ratio $1 : 2 : 3 : 4$.

Solution

Similar Questions

Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. if the first overtone of $ A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B,$ the ratio of the lengths of the strings is

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