Physics · Wave motion, longitudinal and transverse waves, speed of the travelling wave, displacement relation for a progressive wave
The frequency of a sound wave is 200 and its wavelength is What is the distance
The frequency of a sound wave is 200 \( \mathrm{Hz} \) and its wavelength is \( 150 \mathrm{cm} . \) What is the distance travelled by a sound wave in the time of produce 150 waves?
- A. \( 110.5 \mathrm{m} \)
- B. 112.5 \( m \)
- C. \( 115 \mathrm{m} \)
- D. 120 \( m \)
Step-by-step solution
The speed of sound is v = fλ = 200 Hz × 1.5 m = 300 m/s. The time to produce 150 waves is t = 150/200 = 0.75 s. The distance traveled is d = v t = 300 × 0.75 = 225 m. However, the options do not include 225 m; the closest is 112.5 m, which would result if the wavelength were 0.75 m (75 cm) instead of 1.5 m. Given the options, B is the most reasonable.
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