{"id":330446,"date":"2023-01-06T01:25:40","date_gmt":"2023-01-05T19:55:40","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-number-of-possible-natural-oscillations-of-air-column-in-a-pipe-closed-at-one-end-of-length-85-cm-whose-frequencies-lie-below-1250-hz-are-velocity-of-sound-340-m-s-1\/"},"modified":"2025-06-26T18:02:30","modified_gmt":"2025-06-26T12:32:30","slug":"the-number-of-possible-natural-oscillations-of-air-column-in-a-pipe-closed-at-one-end-of-length-85-cm-whose-frequencies-lie-below-1250-hz-are-velocity-of-sound-340-m-s-1","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-number-of-possible-natural-oscillations-of-air-column-in\/","title":{"rendered":"The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m\u00a0s-1)\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m\u00a0s-1)\u00a0","custom_permalink":"question\/physics\/the-number-of-possible-natural-oscillations-of-air-column-in\/"},"categories":[],"acf":{"question":"

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are (Velocity of sound = 340 m s<\/mi>-<\/mo>1<\/mn><\/mrow><\/msup><\/math>) <\/p>","options":[{"option":"

4<\/p>","correct":false},{"option":"

5<\/p>","correct":false},{"option":"

7<\/p>","correct":false},{"option":"

6<\/p>","correct":true}],"solution":"

Fundamental frequency of the closed organ pipe is<\/p>

v<\/mi>=<\/mo>v<\/mi>4<\/mn>L<\/mi><\/mrow><\/mfrac><\/math><\/p>

 Here, <\/mtext>v<\/mi>=<\/mo>340<\/mn> <\/mo>m<\/mi> <\/mo>s<\/mi><\/mrow>-<\/mo>1<\/mn><\/mrow><\/msup>,<\/mo>L<\/mi>=<\/mo>85<\/mn> <\/mo>cm<\/mi>=<\/mo>0<\/mn>.<\/mo>85<\/mn> <\/mo>m<\/mi><\/math><\/p>

\u2234<\/mo>  <\/mo>v<\/mi>=<\/mo>340<\/mn> <\/mo>m<\/mi> <\/mo>s<\/mi><\/mrow>-<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>4<\/mn>\u00d7<\/mo>0<\/mn>.<\/mo>85<\/mn> <\/mo>m<\/mi><\/mrow><\/mfrac>=<\/mo>100<\/mn> <\/mo>Hz<\/mi><\/math><\/p>

The natural frequencies of the closed organ pipe will be<\/p>

v<\/mi>n<\/mi><\/msub>=<\/mo>(<\/mo>2<\/mn>n<\/mi>-<\/mo>1<\/mn>)<\/mo>v<\/mi>=<\/mo>v<\/mi>,<\/mo>3<\/mn>v<\/mi>,<\/mo>5<\/mn>v<\/mi>,<\/mo>7<\/mn>v<\/mi>,<\/mo>9<\/mn>v<\/mi>,<\/mo>11<\/mn>v<\/mi>,<\/mo>13<\/mn>v<\/mi>,<\/mo>\u2026<\/mo><\/math><\/p>

       =<\/mo>100<\/mn> <\/mo>Hz<\/mi>,<\/mo>300<\/mn> <\/mo>Hz<\/mi>,<\/mo>500<\/mn> <\/mo>Hz<\/mi>,<\/mo>700<\/mn> <\/mo>Hz<\/mi>,<\/mo>900<\/mn> <\/mo>Hz<\/mi><\/math><\/p>

                                                 1100<\/mn> <\/mo>Hz<\/mi>,<\/mo>1300<\/mn> <\/mo>Hz<\/mi>,<\/mo>\u2026<\/mo> and so on. <\/mtext><\/math><\/p>

Thus, the natural frequencies lies below the 1250 Hz is 6.<\/p>

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