Superposition and stationary wavesAQA A-Level Physics: Subtopic test

1. 1
   Two wave pulses travel towards each other along a long stretched rope. One is a crest with a maximum displacement of 0.040 m, and the other is a crest with a maximum displacement of 0.030 m, both on the same side of the undisturbed rope. The pulses overlap exactly at one instant and then move apart.

   (a)

   What is the maximum displacement of the rope at the instant when the two pulses overlap exactly?

   [1 mark]

   • A0.010 m
   • B0.035 m
   • C0.050 m
   • D0.070 m

   (b)

   The 0.030 m pulse is replaced by a trough of the same size, a displacement of 0.030 m on the opposite side of the rope. What is the displacement of the rope at the instant the pulses overlap exactly?

   [1 mark]

   • A0.070 m
   • B0.010 m on the same side as the larger pulse
   • C0.010 m on the same side as the smaller pulse
   • DZero

   (c)

   State the principle of superposition and use it to describe what happens to the two original pulses after they have passed through each other.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A guitar string is fixed at both ends and the vibrating length is 0.65 m. The string has mass per unit length 5.0 × 10⁻³ kg m⁻¹ and is under a tension of 80 N. It is plucked so that it vibrates in its first harmonic.

   (a)

   What is the wavelength of the stationary wave on the string in its first harmonic?

   [1 mark]

   • A0.65 m
   • B0.33 m
   • C1.3 m
   • D2.6 m

   (b)

   The frequency of the first harmonic is 97 Hz. What is the frequency of the third harmonic of this string?

   [1 mark]

   • A291 Hz
   • B194 Hz
   • C388 Hz
   • D32 Hz

   (c)

   The tension is increased to 320 N, with the length and mass per unit length unchanged. Calculate the new frequency of the first harmonic.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A microwave transmitter faces a flat metal plate, 0.50 m away, and sets up a stationary wave between the transmitter and the plate. A small microwave detector is moved slowly along the line between them and the signal is found to fall to a minimum at positions that are 1.4 cm apart. The speed of electromagnetic waves is 3.00 × 10⁸ m s⁻¹.

   (a)

   Explain how a stationary wave is formed between the transmitter and the plate.

   [3 marks]

   (b)

   Calculate the wavelength and the frequency of the microwaves.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student investigates how the frequency of the first harmonic of a stationary wave on a stretched metal wire depends on the length l of the vibrating section, the tension T in the wire and the mass per unit length μ of the wire. The wire passes over a pulley and is held in tension by hanging masses. Its vibrating length is set between two bridges, and it is driven by a vibration generator connected to a signal generator whose frequency can be varied.

   (a)

   Describe how the student could investigate how the frequency of the first harmonic depends on the length of the vibrating section, and how the results could be analysed to test the relationship f ∝ 1/l.

   [6 marks]

   (b)

   In one trial the vibrating length is 0.50 m, the tension is 49 N and μ is 4.0 × 10⁻³ kg m⁻¹. Calculate the frequency of the first harmonic and of the third harmonic. The student then wants to double the first harmonic frequency by changing only one of l, T or μ. Determine the change needed in each case and suggest, with a reason, which change is the most practical.

   [6 marks]

   Total for question 4: 12 marks

End of questions