Date | November 2020 | Marks available | 2 | Reference code | 20N.2.SL.TZ0.4 |
Level | Standard level | Paper | Paper 2 | Time zone | 0 - no time zone |
Command term | Estimate | Question number | 4 | Adapted from | N/A |
Question
Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of 850 Hz850Hz. Point P is located 22.5 m from A and 24.3 m from B. The speed of sound is 340 m s-1.
Deduce that a minimum intensity of sound is heard at P.
A microphone moves along the line from P to Q. PQ is normal to the line midway between the loudspeakers.
The intensity of sound is detected by the microphone. Predict the variation of detected intensity as the microphone moves from P to Q.
When both loudspeakers are operating, the intensity of sound recorded at Q is I0. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to IA.
Estimate IAI0.
Markscheme
wavelength=340850=0.40 «m»✓
path difference =1.8 «m» ✓
1.8 «m»=4.5λ OR 1.80.20=9 «half-wavelengths» ✓
waves meet in antiphase «at P»
OR
destructive interference/superposition «at P» ✓
Allow approach where path length is calculated in terms of number of wavelengths; along path A (56.25) and
path B (60.75) for MP2, hence path difference 4.5 wavelengths for MP3
«equally spaced» maxima and minima ✓
a maximum at Q ✓
four «additional» maxima «between P and Q» ✓
the amplitude of sound at Q is halved ✓
«intensity is proportional to amplitude squared hence» IAI0=14 ✓