## Waves, Numerical Problems

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S No | Description of problem |
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Problem 1 | What is the wavelength of a television station which transmits vision on 500 MHz and sound on 505 MHz, respectively? Take the speed of electromagnetic wave 3 × 108 ms^{-1}.See Solution |

Problem 2 | A person on the sea shore observes 48 waves reach the shore in one minute. If the wavelength of the wave is 10 m, find the velocity of the wave. See Solution |

Problem 3 | In a ripple tank 500 waves pass through a certain point in 10 seconds. If the speed of the wave is 3.5 ms-1, find the wavelength of the wave. See Solution |

Problem 4 | A string of guitar 1.3 m long vibrates with 4 nodes, 2 of them at the ends. Find the wavelength and speed of the wave in the string if it vibrates at 500 Hz. See Solution |

Problem 5 | A tension of 400 N causes a 300 g wire of length 1.6 m to vibrate with a frequency of 40 Hz. What is the wavelength of the transverse waves? See Solution |

Problem 6 | Compare the theoretical speeds of sound in Hydrogen (M_{H} = 2.0 g/mol, γ_{H} = 1.4) with helium (M_{He} = 4.0 g/mol, γ_{He} = 1.66 and R = 8334 j k^{-1} mol) at 0°C.See Solution |

Problem 7 | The speed of sound in air at 0^{o}C is 332 ms^{-1}. What will be the speed of sound at 22°C?See Solution |

Problem 8 | Two tuning forks P and Q give 4 beats per second. On loading Q lightly with wax, we get 3 beats per second. What is the frequency of Q before and after loading it if the frequency of P is 512 Hz. See Solution |

Problem 9 | On a sunny day, the speed of sound in the air is 340 m/s. 2 tuning forks A and B are sounded simultaneously. The wavelength of the sound emitted are 1.5 m and 1.68 m respectively. How many beats will produce? See Solution |

Problem 10 | A sound source vibrates at 200 Hz and is receding from a stationary observer at 18 m/s. If the speed of sound is 331 m/s then what frequency does the observer hear? (‘Receding’ means moving away). See Solution |

Problem 11 | Suppose a train that has a 150 Hz horn is moving at 35.0 m/s in still air on day when the speed of sound is 340 m/s. (a) What frequencies are observed by a stationary person at the side of the tracks as the train approaches and after it passes? (b) What frequency is observed by the train’s engineer traveling on the train? See Solution |

Problem 12 | The first over tone of an open organ pipe has the same frequency as the first overtone of a closed pipe 3.6 m in length. What is the length of the open organ pipe? See Solution |

Problem 13 | What length of open pipe will produce a frequency of 1200 Hz as its overtone on a day when the speed of sound is 340 m/s? See Solution |

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