Consider the situation shown in figure.
Question: Consider the situation shown in figure. The wire which has a mass of $4.00 \mathrm{~g}$ oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming that the speed of sound in air is $340 \mathrm{~m} \mathrm{~s}^{-1}$, find the tension in the wire. Solution:...
Read More →A U-tube having unequal arm-lengths has water in it.
Question: A U-tube having unequal arm-lengths has water in it. A tuning fork of frequency $440 \mathrm{~Hz}$ can set up the air in the shorter arm in its fundamental mode of vibration and the same tuning fork can set up the air in the longer arm in its first overtone vibration. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air $=330 \mathrm{~m} \mathrm{} \mathrm{s}^{-1}$. Solution:...
Read More →A piston is fitted in a cylindrical tube of small cross
Question: A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency $512 \mathrm{~Hz}$. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of $32.0 \mathrm{~cm}$. Calculate the speed of sound in the air of the tube. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\left(2 x^{2}-3 x+4\right)^{5}$ Solution:...
Read More →Two successive resonance frequencies
Question: Two successive resonance frequencies in an open organ pipe are $1944 \mathrm{~Hz}$ and $2592 \mathrm{~Hz}$. Find the length of the tube. The speed of sound in air is $324 \mathrm{~ms}^{-1}$. Solution:...
Read More →An electronically driven loudspeaker is placed near the open end
Question: An electronically driven loudspeaker is placed near the open end of a resonance column apparatus. The length of air column in the tube is $80 \mathrm{~cm}$. The frequency of the loudspeaker can be varied between $20 \mathrm{~Hz}$ and $2 \mathrm{kHz}$. Find the frequencies at which the column will resonate. Speed of sound in air $=320 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $(3-4 x)^{5}$ Solution:...
Read More →An open organ pipe has a length of
Question: An open organ pipe has a length of $5 \mathrm{~cm}$. (a) Find the fundamental frequency of vibration of this pipe. (b) What is the highest harmonic of such a tube that is in the audible range? Speed of sound in air is $340 \mathrm{~m} \mathrm{~s}^{-1}$ and the audible range is $20-20,000$ $\mathrm{Hz}$. Solution:...
Read More →Find the greatest length of an organ pipe open
Question: Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range $(20-20,000 \mathrm{~Hz})$. Speed of sound in air $=340 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $(5+7 x)^{6}$ Solution: $=42 \cdot(5+7 x)^{5}$...
Read More →A copper rod of length 1.0 m is clamped at its middle point.
Question: A copper rod of length $1.0 \mathrm{~m}$ is clamped at its middle point. Find the frequencies between $20 \mathrm{~Hz}$ and $20,000 \mathrm{~Hz}$ at which standing longitudinal waves can be set up in the rod. The speed of sound in copper is $3.8 \mathrm{~km} \mathrm{~s}^{-1}$. Solution:...
Read More →The first overtone frequency of a closed organ pipe
Question: The first overtone frequency of a closed organ pipe $P_{1}$ is equal to the fundamental frequency of a open organ pipe $P_{2}$. If the length of the pipe $P_{1}$ is $30 \mathrm{~cm}$, what will be the length of $P_{2}$ ? Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t. $\mathrm{x}$ : $\sqrt{\tan x}$ Solution:...
Read More →In a resonance column experiment,
Question: In a resonance column experiment, a tuning fork of frequency $400 \mathrm{~Hz}$ is used. The first resonance is observed when the air column has a length of $20.0 \mathrm{~cm}$ and the second resonance is observed when the air column has a length of $62.0 \mathrm{~cm}$. (a) Find the speed of sound in air. (b) How much distance above the open end does the pressure node form? Solution:...
Read More →A cylindrical metal tube has a length of
Question: A cylindrical metal tube has a length of $50 \mathrm{~cm}$ and is open at both ends. Find the frequencies between $1000 \mathrm{~Hz}$ and $2000 \mathrm{~Hz}$ at which the air column in the tube can resonate. Speed of sound in air is $340 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : Solution:...
Read More →The separation between a node and the next antinode
Question: The separation between a node and the next antinode in a vibrating air column is $25 \mathrm{~cm}$. If the speed of sound in air is $340 \mathrm{~m}$ $\mathrm{s}^{-1}$, find the frequency of vibration of the air column. Solution:...
Read More →In a standing wave pattern in a vibrating air column,
Question: In a standing wave pattern in a vibrating air column, nodes are formed at a distance of $4.0 \mathrm{~cm}$. If the speed of sound in air is $328 \mathrm{~m} \mathrm{~s}^{-1}$, what is the frequency of the source? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\tan ^{3} x$ Solution:...
Read More →A closed organ pipe can vibrate at a minimum frequency of
Question: A closed organ pipe can vibrate at a minimum frequency of $500 \mathrm{~Hz}$. Find the length of the tube. Speed of sound in air $=340$ $\mathrm{m} \mathrm{s}^{-1}$. Solution:...
Read More →Find the fundamental, first overtone and second overtone frequencies
Question: Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is $340 \mathrm{~ms}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cot ^{2} x$ Solution:...
Read More →Two sources of sound S1 and S2 vibrate at same frequency
Question: Two sources of sound $S_{1}$ and $S_{2}$ vibrate at same frequency and are in phase. The intensity of sound detected at a point $P$ as shown in the figure is $I_{0}$. (a) If $\theta$ equals $45^{\circ}$, what will be the intensity of sound detected at this point if one of the sources is switched off? (b) What will be the answer of the previous part if $\theta=60^{\circ}$ ? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cos x^{3}$ Solution: $=-\sin x^{3} \cdot 3 x^{2}$ $=-3 x^{2} \sin x^{3}$...
Read More →Figure shown two coherent sources S1 and S2
Question: Figure shown two coherent sources $S_{1}$ and $S_{2}$ which emit sound of wavelength $\lambda$ in phase. The separation between the sources is $3 \lambda$. A circular wire of large radius is placed in such way that $S_{1}, S_{2}$ is at the centre of the wire. Find the angular positions $\theta$ on the wire for which constructive interference takes place. Solution:...
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