A sound wave has a frequency of 2 kHz and wave length 35 cm. How long will it take to travel 1.5 km

CONCEPT:

• Wave: It can be defined as the transport of energy without the transport of matter.
• The properties of waves are:
  • Wavelength (λ): The distance between two crests or troughs of a wave is known as wavelength. One wavelength equals the distance between two consecutive crests.
  • Frequency (f): The number of oscillations or the number of waves passes a given point in one sec. Its SI unit is Hertz.
  • Time period (T): The time taken by the wave to complete one cycle.
• The relation between velocity, wavelength and frequency and time period of a wave is

\( ⇒ f = \frac{1}{T} = \frac{v}{\lambda }\;\)

[where f = frequency, T = time period, v = velocity of wave, λ = wavelenght]

CALCULATION:

Given - Frequency (f) = 2 kHz = 2000 Hz and Wavelength (λ) = 35 cm = 0.35 m

• The relation between velocity, wavelength and frequency of a wave is given by 

⇒ v = λ f = 0.35 m × 2000 Hz = 700 m/s

• The time taken by the wave to travel a distance, d of 1.5 km is

⇒ t = d/v = (1.5 x 1000)/700 = 15/7 = 2.1 sec

• Thus sound will take 2.1 s to travel a distance of 1.5 km.