A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms^{-1} at an angle of ${60}^{0}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms^{-1}), is:

1. 100 Hz

2. 103 Hz

3. 106 Hz

4. 97 Hz

Subtopic: Doppler's Effect |

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4.0 gm of gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK^{-1 }mol^{-1}. If the speed of sound in the gas at NTP is 952 ms^{-1}, then the molar heat capacity at constant pressure will be: $\left[TakeR=8.31J{K}^{-1}mo{l}^{-1}\right]$

1. 8.0 JK^{-1} mol^{-1}

2. 7.5 JK^{-1} mol^{-1}

3. 7.0 JK^{-1} mol^{-1}

4. 8.5 JK^{-1} mol^{-1 }

Subtopic: Speed of Sound |

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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:

1. 155 Hz

2. 205 Hz

3. 10.5 Hz

4. 105 Hz

Subtopic: Travelling Wave on String |

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The fundamental frequency of a closed organ pipe of a length 20 cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

1. 80 cm

2. 100 cm

3. 120 cm

4. 140 cm

Subtopic: Standing Waves |

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If n_{1}, n_{2,} and n_{3 }are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by:

1. $\frac{1}{n}=\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}+\frac{1}{{n}_{3}}$

2. $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{{n}_{1}}}+\frac{1}{\sqrt{{n}_{2}}}+\frac{1}{\sqrt{{n}_{3}}}$

3. $\sqrt{n}=\sqrt{{n}_{1}}+\sqrt{{n}_{2}}+\sqrt{{n}_{3}}$

4. $n={n}_{1}+{n}_{2}+{n}_{3}$

Subtopic: Standing Waves |

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The number of possible natural oscillations of the air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are:(Velocity of sound=$340m/s$)

1. 4

2. 5

3. 7

4. 6

Subtopic: Standing Waves |

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A speeding motorcyclist sees a traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be:

1. 1332 Hz

2. 1372 Hz

3. 1412 Hz

4. 1454 Hz

Subtopic: Doppler's Effect |

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If we study the vibration of a pipe open at both ends, then which of the following statements is not true:

1. Odd harmonics of the fundamental frequency will be generated

2. All harmonics of the fundamental frequency will be generated

3. Pressure change will be maximum at both ends

4. The open end will be an antinode

Subtopic: Standing Waves |

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A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency of 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of 513 Hz. The unknown frequency will be:

1. 246 Hz

2. 240 Hz

3. 260 Hz

4. 254 Hz

Subtopic: Beats |

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A wave travelling in the +ve x-direction having maximum displacement along y-direction as 1 m, wavelength $2\pi m$ and frequency of $\frac{1}{\mathrm{\pi}}$ Hz, is represented by:

$1.y=\mathrm{sin}\left(2\pi x-2\pi t\right)$

Subtopic: Wave Motion |

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