Stationary wavesEdexcel International A Level Physics: Subtopic test

1. 1
   A student fixes one end of a long elastic cord to a wall and shakes the other end up and down. At one particular frequency a stationary wave appears on the cord, with the cord appearing still at certain points and vibrating with large amplitude at others.

   (a)

   Which statement correctly describes a node on a stationary wave?

   [1 mark]

   • AA point where the amplitude of vibration is a maximum
   • BA point where the amplitude of vibration is always zero
   • CA point that is momentarily at rest once in each cycle
   • DA point where the wave transfers the greatest amount of energy

   (b)

   Two adjacent nodes on the cord are 0.15 m apart. What is the wavelength of the waves that form the stationary wave?

   [1 mark]

   • A0.075 m
   • B0.15 m
   • C0.30 m
   • D0.60 m

   (c)

   Explain how the stationary wave is formed on the cord.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A guitar string of length 0.60 m and mass per unit length 4.0 × 10⁻⁴ kg m⁻¹ is fixed at both ends. It is held under a tension of 36 N and plucked so that it vibrates in its fundamental mode (one antinode).

   (a)

   Calculate the speed of transverse waves on the string.

   [1 mark]

   • A300 m s⁻¹
   • B150 m s⁻¹
   • C600 m s⁻¹
   • D9.0 × 10⁴ m s⁻¹

   (b)

   What is the frequency of the fundamental mode of this string?

   [1 mark]

   • A125 Hz
   • B500 Hz
   • C750 Hz
   • D250 Hz

   (c)

   The guitarist tightens the string until the tension is 64 N. Calculate the new frequency of the fundamental mode.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In Core Practical 5 a student investigates a string of length 0.80 m and mass per unit length 1.5 × 10⁻³ kg m⁻¹. One end is attached to a vibration generator connected to a signal generator. The string passes over a pulley, and a hanging mass at the other end provides the tension. The student takes g = 9.81 N kg⁻¹.

   (a)

   Describe how the student can find the frequency of the fundamental stationary wave on the string.

   [3 marks]

   (b)

   The hanging mass is 0.50 kg. Calculate the frequency of the fundamental. State and explain the effect on this frequency of increasing the hanging mass to 2.0 kg.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A stringed-instrument maker is choosing strings for a small harp. Each string is 0.65 m long and fixed at both ends, and is tuned by adjusting its tension. String A has a mass per unit length of 5.0 × 10⁻⁴ kg m⁻¹ and is under a tension of 80 N. String B has a mass per unit length of 2.0 × 10⁻³ kg m⁻¹ and is also under a tension of 80 N.

   (a)

   Explain how a stationary wave forms on a string fixed at both ends, and why a string can only vibrate in a stationary wave pattern at certain frequencies. Refer to nodes and antinodes in your answer.

   [6 marks]

   (b)

   Calculate the fundamental frequency of each string. Explain why the two frequencies differ, and calculate the tension needed to make string B give the same fundamental frequency as string A.

   [6 marks]

   Total for question 4: 12 marks

End of questions