354955
In one metre long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \(480\;Hz\). \((v = 320\;m/s)\)
1 Third
2 Fifth
3 Fourth
4 Sixth
Explanation:
In case of open pipe, \(f=\dfrac{n v}{2 l}\) where \(n=\) order of harmonics \(=\) order of mode of vibration \(\Rightarrow n=\dfrac{f \times 2 l}{v}\) \( = \frac{{480}}{{320}} \times 2 \times 1 = 3\;\;\;{\mkern 1mu} {\kern 1pt} [{\text{ Here }}v = 320\;m/s]\)
PHXI15:WAVES
354956
An organ pipe \({P_{1}}\) closed at one end is vibrating in its first overtone, and another pipe \({P_{2}}\), open at both ends, is vibrating in its second overtone. Both organ pipes are in resonance. The ratio of length of pipes \({P_{1}}\) and \({P_{2}}\) is
1 1
2 \({1: 2}\)
3 \({1: 3}\)
4 \({3: 4}\)
Explanation:
At resonance, first overtone of closed pipe \({=}\) second overtone of open pipe \({3 \times \dfrac{v}{4 L_{1}}=\dfrac{3}{2 L_{2}} v}\) \(\dfrac{4}{4 L_{1}}=\dfrac{1}{2 L_{2}}\) \(\dfrac{L_{1}}{L_{2}}=\dfrac{2}{4}=1: 2\)
PHXI15:WAVES
354957
In open organ pipe, if fundamental frequency is, \(n\) then the other frequencies are
1 \(n, 2 n, 3 n, 4 n\)
2 \(n,{\text{ }}2n,{\text{ }}4n,{\text{ }}8n\)
3 \(n, 3 n, 5 n\)
4 None of these
Explanation:
In open pipe at both ends, the natural frequencies of oscillation from a harmonic series that includes all integrals multiples of the fundamental frequency, i.e. all even odd harmonics are present. Therefore, if fundamental frequency is \(n\), then other frequencies are \(n, 2 n, 3 n, 4 n, \ldots\),
PHXI15:WAVES
354958
Two adjacent natural frequencies of an organ pipe are formed to be 550 \(Hz\) and 650 \(Hz\) . Calculate the length of this pipe. (Velocity of sound in air \(350 {~m} / {s}\) ).
1 \(3.27\,m\)
2 \(1.75\,m\)
3 \(5.24\,m\)
4 \(7.51\,m\)
Explanation:
In case of open organ pipe we have all types of harmonic, even as well as odd. While in case of close organ pipe we have only odd harmonic. The ratio of two adjacent frequencies \(\dfrac{f_{n}}{f_{n+1}}=\dfrac{550}{650}=\dfrac{50 \times 11}{50 \times 13}=\dfrac{11}{13}\) Hence the adjacent harmonic are 11th and 13th. Both harmonic are odd hence frequency it is the case of close organ pipe. Clearly, the fundamental frequency should be 50 Hz . The fundamental frequency in case of close organ pipe \(f_{0}=\dfrac{v}{4 l} \Rightarrow 50=\dfrac{350}{4 \times l}\) Hence length of the pipe \(l=\dfrac{350}{50 \times 4}=1.75 {~m}\)
354955
In one metre long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \(480\;Hz\). \((v = 320\;m/s)\)
1 Third
2 Fifth
3 Fourth
4 Sixth
Explanation:
In case of open pipe, \(f=\dfrac{n v}{2 l}\) where \(n=\) order of harmonics \(=\) order of mode of vibration \(\Rightarrow n=\dfrac{f \times 2 l}{v}\) \( = \frac{{480}}{{320}} \times 2 \times 1 = 3\;\;\;{\mkern 1mu} {\kern 1pt} [{\text{ Here }}v = 320\;m/s]\)
PHXI15:WAVES
354956
An organ pipe \({P_{1}}\) closed at one end is vibrating in its first overtone, and another pipe \({P_{2}}\), open at both ends, is vibrating in its second overtone. Both organ pipes are in resonance. The ratio of length of pipes \({P_{1}}\) and \({P_{2}}\) is
1 1
2 \({1: 2}\)
3 \({1: 3}\)
4 \({3: 4}\)
Explanation:
At resonance, first overtone of closed pipe \({=}\) second overtone of open pipe \({3 \times \dfrac{v}{4 L_{1}}=\dfrac{3}{2 L_{2}} v}\) \(\dfrac{4}{4 L_{1}}=\dfrac{1}{2 L_{2}}\) \(\dfrac{L_{1}}{L_{2}}=\dfrac{2}{4}=1: 2\)
PHXI15:WAVES
354957
In open organ pipe, if fundamental frequency is, \(n\) then the other frequencies are
1 \(n, 2 n, 3 n, 4 n\)
2 \(n,{\text{ }}2n,{\text{ }}4n,{\text{ }}8n\)
3 \(n, 3 n, 5 n\)
4 None of these
Explanation:
In open pipe at both ends, the natural frequencies of oscillation from a harmonic series that includes all integrals multiples of the fundamental frequency, i.e. all even odd harmonics are present. Therefore, if fundamental frequency is \(n\), then other frequencies are \(n, 2 n, 3 n, 4 n, \ldots\),
PHXI15:WAVES
354958
Two adjacent natural frequencies of an organ pipe are formed to be 550 \(Hz\) and 650 \(Hz\) . Calculate the length of this pipe. (Velocity of sound in air \(350 {~m} / {s}\) ).
1 \(3.27\,m\)
2 \(1.75\,m\)
3 \(5.24\,m\)
4 \(7.51\,m\)
Explanation:
In case of open organ pipe we have all types of harmonic, even as well as odd. While in case of close organ pipe we have only odd harmonic. The ratio of two adjacent frequencies \(\dfrac{f_{n}}{f_{n+1}}=\dfrac{550}{650}=\dfrac{50 \times 11}{50 \times 13}=\dfrac{11}{13}\) Hence the adjacent harmonic are 11th and 13th. Both harmonic are odd hence frequency it is the case of close organ pipe. Clearly, the fundamental frequency should be 50 Hz . The fundamental frequency in case of close organ pipe \(f_{0}=\dfrac{v}{4 l} \Rightarrow 50=\dfrac{350}{4 \times l}\) Hence length of the pipe \(l=\dfrac{350}{50 \times 4}=1.75 {~m}\)
354955
In one metre long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \(480\;Hz\). \((v = 320\;m/s)\)
1 Third
2 Fifth
3 Fourth
4 Sixth
Explanation:
In case of open pipe, \(f=\dfrac{n v}{2 l}\) where \(n=\) order of harmonics \(=\) order of mode of vibration \(\Rightarrow n=\dfrac{f \times 2 l}{v}\) \( = \frac{{480}}{{320}} \times 2 \times 1 = 3\;\;\;{\mkern 1mu} {\kern 1pt} [{\text{ Here }}v = 320\;m/s]\)
PHXI15:WAVES
354956
An organ pipe \({P_{1}}\) closed at one end is vibrating in its first overtone, and another pipe \({P_{2}}\), open at both ends, is vibrating in its second overtone. Both organ pipes are in resonance. The ratio of length of pipes \({P_{1}}\) and \({P_{2}}\) is
1 1
2 \({1: 2}\)
3 \({1: 3}\)
4 \({3: 4}\)
Explanation:
At resonance, first overtone of closed pipe \({=}\) second overtone of open pipe \({3 \times \dfrac{v}{4 L_{1}}=\dfrac{3}{2 L_{2}} v}\) \(\dfrac{4}{4 L_{1}}=\dfrac{1}{2 L_{2}}\) \(\dfrac{L_{1}}{L_{2}}=\dfrac{2}{4}=1: 2\)
PHXI15:WAVES
354957
In open organ pipe, if fundamental frequency is, \(n\) then the other frequencies are
1 \(n, 2 n, 3 n, 4 n\)
2 \(n,{\text{ }}2n,{\text{ }}4n,{\text{ }}8n\)
3 \(n, 3 n, 5 n\)
4 None of these
Explanation:
In open pipe at both ends, the natural frequencies of oscillation from a harmonic series that includes all integrals multiples of the fundamental frequency, i.e. all even odd harmonics are present. Therefore, if fundamental frequency is \(n\), then other frequencies are \(n, 2 n, 3 n, 4 n, \ldots\),
PHXI15:WAVES
354958
Two adjacent natural frequencies of an organ pipe are formed to be 550 \(Hz\) and 650 \(Hz\) . Calculate the length of this pipe. (Velocity of sound in air \(350 {~m} / {s}\) ).
1 \(3.27\,m\)
2 \(1.75\,m\)
3 \(5.24\,m\)
4 \(7.51\,m\)
Explanation:
In case of open organ pipe we have all types of harmonic, even as well as odd. While in case of close organ pipe we have only odd harmonic. The ratio of two adjacent frequencies \(\dfrac{f_{n}}{f_{n+1}}=\dfrac{550}{650}=\dfrac{50 \times 11}{50 \times 13}=\dfrac{11}{13}\) Hence the adjacent harmonic are 11th and 13th. Both harmonic are odd hence frequency it is the case of close organ pipe. Clearly, the fundamental frequency should be 50 Hz . The fundamental frequency in case of close organ pipe \(f_{0}=\dfrac{v}{4 l} \Rightarrow 50=\dfrac{350}{4 \times l}\) Hence length of the pipe \(l=\dfrac{350}{50 \times 4}=1.75 {~m}\)
354955
In one metre long open pipe what is the harmonic of resonance obtained with a tuning fork of frequency \(480\;Hz\). \((v = 320\;m/s)\)
1 Third
2 Fifth
3 Fourth
4 Sixth
Explanation:
In case of open pipe, \(f=\dfrac{n v}{2 l}\) where \(n=\) order of harmonics \(=\) order of mode of vibration \(\Rightarrow n=\dfrac{f \times 2 l}{v}\) \( = \frac{{480}}{{320}} \times 2 \times 1 = 3\;\;\;{\mkern 1mu} {\kern 1pt} [{\text{ Here }}v = 320\;m/s]\)
PHXI15:WAVES
354956
An organ pipe \({P_{1}}\) closed at one end is vibrating in its first overtone, and another pipe \({P_{2}}\), open at both ends, is vibrating in its second overtone. Both organ pipes are in resonance. The ratio of length of pipes \({P_{1}}\) and \({P_{2}}\) is
1 1
2 \({1: 2}\)
3 \({1: 3}\)
4 \({3: 4}\)
Explanation:
At resonance, first overtone of closed pipe \({=}\) second overtone of open pipe \({3 \times \dfrac{v}{4 L_{1}}=\dfrac{3}{2 L_{2}} v}\) \(\dfrac{4}{4 L_{1}}=\dfrac{1}{2 L_{2}}\) \(\dfrac{L_{1}}{L_{2}}=\dfrac{2}{4}=1: 2\)
PHXI15:WAVES
354957
In open organ pipe, if fundamental frequency is, \(n\) then the other frequencies are
1 \(n, 2 n, 3 n, 4 n\)
2 \(n,{\text{ }}2n,{\text{ }}4n,{\text{ }}8n\)
3 \(n, 3 n, 5 n\)
4 None of these
Explanation:
In open pipe at both ends, the natural frequencies of oscillation from a harmonic series that includes all integrals multiples of the fundamental frequency, i.e. all even odd harmonics are present. Therefore, if fundamental frequency is \(n\), then other frequencies are \(n, 2 n, 3 n, 4 n, \ldots\),
PHXI15:WAVES
354958
Two adjacent natural frequencies of an organ pipe are formed to be 550 \(Hz\) and 650 \(Hz\) . Calculate the length of this pipe. (Velocity of sound in air \(350 {~m} / {s}\) ).
1 \(3.27\,m\)
2 \(1.75\,m\)
3 \(5.24\,m\)
4 \(7.51\,m\)
Explanation:
In case of open organ pipe we have all types of harmonic, even as well as odd. While in case of close organ pipe we have only odd harmonic. The ratio of two adjacent frequencies \(\dfrac{f_{n}}{f_{n+1}}=\dfrac{550}{650}=\dfrac{50 \times 11}{50 \times 13}=\dfrac{11}{13}\) Hence the adjacent harmonic are 11th and 13th. Both harmonic are odd hence frequency it is the case of close organ pipe. Clearly, the fundamental frequency should be 50 Hz . The fundamental frequency in case of close organ pipe \(f_{0}=\dfrac{v}{4 l} \Rightarrow 50=\dfrac{350}{4 \times l}\) Hence length of the pipe \(l=\dfrac{350}{50 \times 4}=1.75 {~m}\)
