**Question 1**

Considering a transverse wave, explain the following terms | |

a) | crest and trough |

b) | amplitude |

c) | frequency |

d) | wavelength |

e) | velocity of propagation. |

**Question 2**

Explain the following terms (using diagrams where necessary): | |

a) | interference |

b) | diffraction |

c) | refraction. |

**Question 3**

Calculate the frequency of | |

a) | red light of wavelength 650nm |

b) | violet light of wavelength 420nm |

**Question 4**

What is the wavelength of x rays of frequency 3×10^{18}Hz |

**Question 5**

What is the wavelength of sound of frequency 440Hz. The speed of sound in air is about 340ms^{-1}. |

**Question 6**

A transverse wave of frequency 5Hz moves along a spring at a speed of 1ms^{-1}. At t = 0 seconds, point p on the spring is at it’s maximum displacement of +2cm. Points A, B and C are points further along the spring (in the direction of motion of the wave). | |

distance p-A = 0.4m | |

distance p-B = 0.5m | |

distance p-C = 0.55m | |

Find the displacements of points A, B and C at | |

a) | t = 0 |

b) | t = 0.2s |

c) | t = 0.25s |

d) | t = 0.3s |

**Question 7**

A tube, closed at one end, is found to have a fundamental frequency of resonance of f_{o} = 200Hz. The length of the tube is 40cm | |

a) | Calculate the speed of sound in the tube |

b) | What is the wavelength of the sound at resonance (frequency, f_{o}). |

c) | What are the frequencies of the next two harmonics of the same tube? |

**Question 8**

The diagram below shows a stationary wave on a wire under tension. The frequency of the oscillations is 1200Hz. | ||

a) | If the length of the wire is 40cm, calculate the speed of the waves moving along it. | |

b) | What will happen to the speed of waves moving along the wire if | |

i) | the tension is doubled (all other factors remaining the same) | |

ii) | the length is doubled (all other factors remaining the same)? |

**Question 9**

A tuning fork is held near the open end of a pipe which is closed at the other end. The fork is vibrating at 440Hz. The length of the air column in the pipe is varied. The first resonance is heard when the length of the pipe is 18.75cm. | |

a) | What is the next length at which resonance will be heard (with the same tuning fork)? |

b) | Calculate the speed of sound in the pipe. |

**Question 10**

a) | Two pipes are closed at one end and open at the other end. One pipe has a length of 30cm and the other has a length of 30·5cm. The pipes have the same diameter and therefore the same "end-correction" of 0·5cm. Calculate the beat frequency which would be heard if both the pipes are caused to resonate at | |

i) | their fundamental frequency (first harmonic) | |

ii) | their first overtone (second harmonic). (Assume the speed of sound is 330ms^{-1}) | |

b) | Explain why beats would not be heard if two pipes having lengths of 30cm and 60cm were sounded together. |

**Question 11**

A transverse sinusoidal wave is represented by the following equation | |

y = 0·2sin(20t - 0·1x)
| |

Assuming that the units of the quantities in the equation are metres and seconds, find | |

a) | the amplitude of the wave |

b) | the wavelength |

c) | the time period |

d) | the velocity of propagation (state the direction of propagation) |

e) | the average transverse speed of a particle in the medium through which the wave is moving. |