Waves on a string

• What is the topic of the video discussed?

  Waves on a string
• What are the two types of waves mentioned?

  Transverse waves and longitudinal waves
• How do transverse waves move?

  Up and down the string
• What is the relationship between oscillations and wave direction in transverse waves?

  Oscillations are perpendicular to wave direction
• What type of wave is produced when the string vibrates?

  A longitudinal wave
• What do transverse and longitudinal waves have in common?

  They have the same frequency
• What happens when waves reflect at the end of the string?

  They interfere and create stationary waves
• What is a stationary wave?

  A wave that does not travel, but vibrates in place
• What is the fundamental frequency in terms of string vibration?

  It is one single loop of vibration
• How is the length of the string related to the fundamental frequency?

  Length equals half a wavelength
• What are nodes and antinodes in a stationary wave?

  Nodes have zero amplitude; antinodes have maximum amplitude
• What is the formula for the wavelength in the fundamental mode?

  Wavelength equals two times the length of the string
• If a guitar string is 85 cm long, what is the wavelength in the fundamental mode?

  $170 \text{ cm}$
• What factors affect the velocity of waves on a string?

  Tension and mass per unit length
• What is the equation for the velocity of a stationary wave?

  $v =$$\sqrt{\frac{t}{\mu}}$
• If the tension in a string is 49 N and the mass per unit length is 0.00057 kg/m, what is the velocity?

  $92.7 \text{ m/s}$
• How do you calculate the wavelength in the fundamental mode for a string length of 32.5 cm?

  $0.65 \text{ m}$
• How do you calculate the frequency of a wave?

  $f =$$\frac{v}{\lambda}$
• If the velocity is 92.7 m/s and the wavelength is 0.65 m, what is the frequency?

  $143 \text{ Hz}$
• What is the significance of writing down the equation in calculations?

  It helps to show the method used
• What happens to the frequency when the tension in the string changes?

  The frequency changes as the velocity changes
• What is the velocity of waves on an electric guitar string with a tension of 76 N and mass per unit length of 0.0068 kg/m?

  $106 \text{ m/s}$
• If the length of the electric guitar string is 1.3 m, what is the wavelength?

  $1.3 \text{ m}$
• What is the frequency of the electric guitar string with a velocity of 106 m/s and wavelength of 1.3 m?

  $81.3 \text{ Hz}$
• What are the harmonics produced by a vibrating string?

  • Fundamental frequency (first harmonic): 1 loop
  • Second harmonic: 2 loops
  • Third harmonic: 3 loops
  • Higher harmonics: additional loops
• What is the relationship between tension, mass per unit length, and wave velocity?

  • Velocity increases with higher tension
  • Velocity decreases with higher mass per unit length
  • Velocity is calculated using $v =$$\sqrt{\frac{t}{\mu}}$