Question

1. How is the vibration of the source related to a wave's frequency?
2. How is wavelength related to frequency for waves moving at a constant speed?
3. How is energy of a wave related to its amplitude?
4. Describe two ways you could measure the wavelength of a longitudinal wave.
5. Describe how you measure the amplitude of a transverse wave.
6. If a wave's period doubles, how does the wave's frequency change?

Answer 1

1. The wave’s frequency equals the source’s vibration frequency. Each complete vibration of the source produces one wave cycle, so faster source vibrations produce a higher wave frequency (f = 1/T).

2. For constant wave speed v, v = f·λ (where λ is wavelength). So wavelength and frequency are inversely related: λ = v / f. If f increases (with v fixed) λ decreases.

3. The energy carried by a wave is proportional to the square of its amplitude: Energy ∝ A^2 (so doubling amplitude gives four times the energy/intensity, for typical mechanical and electromagnetic waves’ intensities).

4. Two ways to measure the wavelength of a longitudinal wave:
- Direct spatial measurement: map the positions of successive compressions (or rarefactions) and measure the distance between them (distance between adjacent compressions = λ).
- Indirect use of speed and frequency: measure the wave speed (e.g., speed of sound in the medium) and the frequency, then compute λ = v / f. (Alternatively, use resonance in a tube and measure spacing between resonance lengths to infer λ.)

5. To measure the amplitude of a transverse wave: measure the maximum displacement of the medium from its equilibrium position — e.g., the vertical distance from the rest line to a crest (or to a trough). This can be done with a ruler, camera/graph, or by reading the peak value on an oscilloscope for electrical analogs.

6. If the period doubles, the frequency halves (since f = 1/T).