Question

A sound wave has a frequency of 2 KHz and wavelength 35 cm. The time taken by it to travel a distance of 7 km will be :

• A. 2.10 s
• B. 1 s
• C. 10.2 s
• D. 10 s

Hint:

1. Ensure all units are SI: Frequency \(f = 2 \text{ KHz} = 2000 \text{ Hz}\). Wavelength \(\lambda = 35 \text{ cm} = 0.35 \text{ m}\). Distance \(d_{travel} = 7 \text{ km} = 7000 \text{ m}\). 2. Calculate wave speed: \(v = f \times \lambda\). \(v = 2000 \times 0.35 = 700 \text{ m/s}\). 3. Calculate time: \(t = \text{distance} / \text{speed}\). \(t = 7000 / 700 = 10 \text{ s}\).

Answer 1

The Correct Option is D

Concept: The relationship between the speed of a wave (\(v\)), its frequency (\(f\)), and its wavelength (\(\lambda\)) is given by \(v = f\lambda\). Also, time taken (\(t\)) to travel a distance (\(d\)) with a constant speed (\(v\)) is given by \(t = \frac{d}{v}\). Step 1: Convert given quantities to SI units
Frequency (\(f\)): 2 KHz (kilohertz) \(1 \text{ KHz} = 1000 \text{ Hz}\) So, \(f = 2 \times 1000 \text{ Hz} = 2000 \text{ Hz}\) (or \(2000 \text{ s}^{-1}\)).
Wavelength (\(\lambda\)): 35 cm (centimeters) \(1 \text{ cm} = 0.01 \text{ m}\) So, \(\lambda = 35 \times 0.01 \text{ m} = 0.35 \text{ m}\).
Distance to travel (\(d_{travel}\)): 7 km (kilometers) \(1 \text{ km} = 1000 \text{ m}\) So, \(d_{travel} = 7 \times 1000 \text{ m} = 7000 \text{ m}\). Step 2: Calculate the speed of the sound wave (\(v\)) Using the formula \(v = f\lambda\): \[ v = (2000 \text{ Hz}) \times (0.35 \text{ m}) \] \[ v = 2000 \times \frac{35}{100} \text{ m/s} \] \[ v = 20 \times 35 \text{ m/s} \] \[ v = 700 \text{ m/s} \] Step 3: Calculate the time taken to travel the given distance Using the formula \(t = \frac{d_{travel}}{v}\): Distance \(d_{travel} = 7000 \text{ m}\) Speed \(v = 700 \text{ m/s}\) \[ t = \frac{7000 \text{ m}}{700 \text{ m/s}} \] \[ t = \frac{70}{7} \text{ s} \] \[ t = 10 \text{ s} \] The time taken by the sound wave to travel 7 km is 10 seconds. This matches option (4).